As an Aerospace Engineering student, I took almost all of those courses. I just realized I know a lot more math than I thought. Your exposition is awesome.
My advice is to study aerospace engineering only if you are passionate about the aviation/space world. Have a clear vision of what you want to achieve, be it working in your dream company, the job you will have or your future lifestyle. The undergraduate degree is sort of an introduction to all fields of aeronautics. It will be up to you to decide what you're going to specialize in, and how. Doing a master's degree, learning in a company as an intern or on your own. Some students will become aerodynamicists, some structural engineers, some materials engineers, control systems engineers, airport engineers, etc. Get my point? When you specialize, you will work with only a few of the things you will have learned in college, but all of them will be somehow connected in the company. It's not about how much math you will use in your working life, but that you need to have mathematical tools for all possible applications in the aeronautical world. In real life, as Tamer says, a computer will take care of calculations. I shall add that you learn math in order to train your mind and prove you can put in the work. Take care and be passionate!
I thought my master's degree didn't involve that much math, because I am a medical engineer. But after watching the video, I noticed that I've completed about 80% of what you mentioned.
@@tienhung3112 We use actually a lot of math, because we are working with fluidic models, biomechanic forces, differential equations for dynamic systems, complex numbers for electrical engineering, fourier transform for MRT reconstruction & spectra. It's also quite important to get the models into programmed applications.
@@realdotty5356 Medical engineering is an interdisciplinary study program with focus on mechanical, electrical engineering and informatics combined with medical contents. Typical fields for work are medical imaging for MRI/CT scans, active and passive implants and other hospital-/laboratory devices.
As a graduate engineer, I can say, core material of math classes are for building the way of thinking and perspective which can incredibly useful in advanced degree and professional life.
Understanding the underlying problems will help you think about things that happen when you make higher level actions. Which is way more important to engineering then anything else.
@@YuTEM yes, this literally applies to anything, look at medicine, a substance can treat a symptom but if you don't treat the cause of the symptom are you really treating the person? Or music, when writing a song you don't just look at "the next 3 notes" a good song feels complete if it all works together, or mathematics, focusing on solving just a single specific problem isn't very useful, the usefulness comes form understanding the general solution to the general problem, and so on...
As a mathematician, I must say I don't use these classes very often either, but what I absolutely value from them is their significance in the development of my problem solving skills, which at the end of the day is what we (engineers and mathematicians alike) essentially are, is problem solvers.
The point of certain algorithms is to know which one to use and understand A statistician can know normal distribution best but what happens when the model cannot be approximated by normal distribution? You need to either design your own distribution or understand that the model fits something else instead. But notice you’re not expected to compute out everything (mean, median, std dev) the computer will do that for you but your numbers are meaningless if you compute with normal instead of the more accurate model
As someone who has taken calc 1, 2, 3, differential equations, and linear algebra, and is going into my junior year of aerospace engineering, I can say that I haven’t taken a single class in my major that didn’t involve math, including calculus. Math is used all the time in school for engineering and we use Matlab in all lab courses. Math is definitely a crucial part of engineering and in my opinion makes it more fun! Math can be very useful in industry for doing hand calculations and for checking code, but often times math is done by computer programs such as ANSYS or Matlab. However, it’s still important to understand the fundamentals of where everything comes from, which requires all levels of calculus.
@@jayevans6146 I have yet to get a real engineering job, so I can’t give you an accurate answer. I did an internship though and the engineers used math and calculus to verify that their code was working properly. As the video states, many types of software exists to help with engineering, but it is definitely useful to know the science and math behind the software to verify that it works properly.
@@infinitespace8313 It was mostly rhetorical. I already know. In reality, about 5%-10% of your actual job will involve actual higher level math/Cal DEs etc
@@jayevans6146 but even then if you didn't learn about those higher level math in school then you wouldn't know it in industry. Even if something constitutes only 1% of your job, you should still be learning of what it is and how it works rather than not knowing it. Of course there is the obvious time investment as these higher level classes take much longer to learn due to their difficulty, but even so if it is used in the field no matter how miniscule you should still learn it in school
@@jayevans6146 Not every engineering field is the same, aerospace is one of the strongest if not the strongest math related engineering, biotech, nano, biomedical, systems, industrial engineers may not need the same amount of math than aerospace
Engineering school doesn't give you every tool you need but it fills your box up with a lot of tools and ways to think about the world. You need the math to really be able to apply concepts in a broad sense. In my field, I use a ton of heavy math. I learned a large part of my math and numerical analysis skills in engineering school. You are also learning different thought paradigms as some others have mentioned, and a rigorous mathematics education is essential to those paradigms.
Yes. I also noticed that in the American system one can enter a PHD program with only a bachelors and sufficient research experience, whereas for England, and I presume also italy, one must have a masters before being admitted into the PHD. Is this true of Italy?
@@randallmcgrath9345 This is true in America, but the PhD program is usually longer, and would be almost equal to getting your master's along the way. Having your master's and then getting a PhD is probably still the more popular route in the US and of similar length in the grand scheme of graduate studies.
A great overview. I found engineering maths very difficult, but luckily the real world was much more software and ‘Pilot/POC’ based. That’s partly because the simplifications needed to make mathematical models work don’t give reliable answers. I saw this from stress analysis for rocket design (where FEA was used) to avionic circuit design. Having said that engineering is all about learning to problem solve and learning to learn, and engineering maths trains you in both. All problems I’ve ever solved seem less confronting than solving a second order non-linear differential equation! Ironically the number one job most engineers quickly find themselves in is leading teams and dealing with people, something many engineering degrees ignore!
We had both differential and integral calculus in one semester and calculus 2 was already multivariable calculus. But instead of being called calculus it was called mathematics for applied sciences, because the class actually called calculus was too pure for applied sciences majors. I'm a CS major and I think around half of our classes are math.
Thanks for sharing and that makes sense. Computer science majors at my school were under the faculty of mathematics…so it makes sense that there’s so much math involved in CS.
A prof in alexanderia U once said, not all math have been you studied in the university you will use it, you just need few basic topics, but studying math build your muscles to "understand anything tough" 💪💪
The only thing that the math serves for engineers is that there is an appreciation that the models you are using in simulation are reasonably approximated. It is near universal that math in your every day engineering job doesn't really go much farther than some basic algebra and trigonometry. We appreciate the math majors and engineers that work together that make the CAD software a reality which helps everybody else's jobs become much easier.
It's not only that. You also need people to build the software to begin with. I worked in civil engineering in a firm where we did A LOT of in-house model building. So yeah, the math was used frequently when building the tools. Less when using them.
as a civil engineer on my 4th year, I realized I was mostly doing the basic algebra math's, very few calculus or non at all around the 3/4 years so it kind of depends on your major, if you choose mechanical u might have to apply more calculus equations and stuff along with algebra so yeah.
Engineering is strange in the fact that you can skate by a whole degree without fully understanding derivations of the equations as long as you know how to apply them. However, if you want a deeper understanding it is very essential you try to understand the foundations on which the concepts were built aka the mathematics. Then you will be able to understand the engineering concept in its entirety which will help guide decision making in later engineering problems.
@@12degreesnowman11 If you master calculus 1/2, physics, and differential equations you will have the best intuition when you get to the applied classes.
@@santiago_moralesduarte The complex number system is a field and for that, at the introductory level, the definition i=\sqrt{-1} is really a very poor definition. Nice for high school level, not for serious college level. I vehemently agree with Abdusselam and that's how we learned it too. In fact, our notation was (0,1)x(0,1)=(-1,0)
I remember when I studied signal and systems, I feel very good about the Fourier series and the math, but I feel it was pretty tricky later on to a class called communication system, which introduce a lot of digital modulation theories. And after this, we have DSP, which is even harder than signal and system
I’m a Chem E and my father is a mechanical engineer, he despises the younger generation of engineers, from his point of view none of them can do the math off the top of their heads or complete drawings without computer assistance. I’ll admit he’s old, like real old lol! But he kind of has a point. For lot of these kids coming through the pipeline I’m personally not confident in their abilities to perform on the job, even after a couple years of training they aren’t up to standards enough to take on larger projects, it’s like they get comfortable in their niche and they stay there and the curiosity about the job just falls off. Every so often there’s one or two rockstars that come out of college but at the rate society is going, every year university standards drop further and further to the point that I really do worry about the future of the career field over all in every discipline. Universities really should re-up the rigor because it’s causing a quality issue to some extent.
A lot of these topics weren't even courses in my college, we just learned about them when we needed them like laplace transform in circuit analysis, and fourier series in intro to signal processing
Hey great video, mechanical engineer here with some additions: Fourier analysis actually is also quite important for mechanical engineering, namely vibrations. Vibrations can cause materials to fatigue, it can be used to monitor the structural health of e.g. bridges (lower stiffness of beams result in a shifting eigenfrequency), vibrations can be countered using Fourier analysis (see the Bambu lab x1 carbon 3D printer, which has active vibration control). It is also important for mathematically modeling systems. Here I am only touching the surface of how much practical use there is for vibrations. It is a technical field on it own really. Calculus 3 does have its practical use. It comes back in fluid dynamics, gravity fields, aerodynamics, electromechanics. E.g. vector fields can describe the flow of a fluid or the effect of gravity on a object moving through space. Hope that helps.
I have a lot of introductory engineer students taking the Calculus sequence. Not all students are that good in math and some complain why they need all that math. And then a bit later there is this field called fluid dynamics...oh yeah baby!
Crazy how different it is in Belgium, computer engineering is more like a mix of computer science and engineering here. Calc 2 is named calc 1 here and it included ODE's and series, calc 2 is multivariable analysis and calc 3 is vector analysis, PDE's and a bit of complex analysis. All engineering majors have to take statistics, discrete math intro and probability. As a CS/E student I have a lot of courses which include fourier and laplace transforms and z transforms such as signal processing, deterministic and stochastic signals and systems. And of course a lot of boolean algebra in courses like digital electronics and discrete mathematics.
Greetings from Brazil. I studied everything mentioned in the video. And indeed, after graduating from college, I've rarely studied all the complex math I learned in college. Currently I work on the power distribution system. In the future I intend to go into projects, where I will be able to apply more of the engineering I learned.
I have been an electronics engineer for about 20 years and I can say Physics and applied math is the most important. Things like finding out how to setup a timer register in a microcontroller or doing a conversion from a A/D converter to a value that means something example(temperature) is majority of the math I use. Finding out how much power is needed and how thick the traces on the circuit board needs to be, are other examples of applied math i have used. I think sometimes colleges over emphasize math and it can scare people away from engineering. Creativity, problem solving, and being able to take an idea to a product is more important. Saying that, being exposed to different math ideas is also useful, but you do not need to be an expert. At the end of the day in the real world, what matters is how good you are at solving a problem and coming up with an idea and able to take that idea and use it.
Probably should mention about how complex analysis is fundamental to field theories - as the conformal mapping and superimposition allows all sorts of analysis (eg inviscid and incompressible flows and EM field)
In Germany we have nearly all of these math concepts included in three courses, called Higher Math 1, 2 and 3, which you have to do in the first three semesters of your studies. Also I can say, that you need most of these math concepts in later courses to describe and calculate with the formulas in the given topic. Especially differential equation will pop up everywhere. So it is kind of helpful to learn all of that in the beginning and than apply that in later courses. So if you wanna go into research it's quite helpful to understand the underlying math of the equations and formulas you are working with. Great vids! It's fun to hear about the experience of engineering students from other countries.
@@samuellandos785 Bei euch ist das heutzutage sowieso alles anders. Als ich studiert habe (Ende der Diplom-Ära) hieß das alles anders, war extrem konzentriert in wenige Vorlesungen und Prüfungen, und reichte *viel* weiter als bei euch heutzutage. Im Ingenieurwesen wurde in den letzten 15-20 Jahren so einiges an mathematischem und physikalischem Tiefgang gestrichen bzw. als Wahlpflicht ausgegliedert. Auf der anderen Seite werdet ihr aber auch extrem gegängelt. Bei mir gab es noch etwas, das hieß "Grundstudium" und ich mußte Scheine machen. Wortwörtlich Scheine. Zettel. Analoges Papier ;-) Die hat man ausgestellt bekommen, wie Akten fakturiert, und irgendwann als Stapel der ollen häßlichen Zicke im Prüfungsamt auf den Tisch gelegt, um zu den Klausuren der Diplom-Vorprüfung zugelassen zu werden. Wenn man das Grundstudium geschafft hatte, wiederholte sich dieses unverschulte, unbegleitete, frei vom Studenten zu gestaltende Verfahren bis zur Ablegung der Diplom-Hauptprüfung. Die Noten des Grundstudiums wurden nie wieder gesehen. Die Endnote berechnete sich nur aus den Prüfungsteilen des Hauptstudiums.
@@bobbwc7011 Das ist so typisches früher war alles besser Gelaber. Beweise doch dass es früher tiefer ging als heute mal abgesehen dass das vom Standort abhängt. Es ist eigentlich eher umgekehrt. Heute werden die Grundlagen aller fachähnlichen Diplomstudiengänge in ein Bachelorstudium gepfercht.
I have spent most of my life working with patents, largely in the area of communications, and most recently in artificial intelligence. I cannot begin to emphasize how important a good, solid understanding of advanced mathematics has been to me.
What I find very interesting is that a lot of these courses are mashed together at the university where I study. Calculus I and II are Higher Mathematics I, linear algebra is Higher Mathematics II and Calculus III, differential equations and partial differential equations is Higher Mathematics III for example
I’m going to use this video as a check list. I just finished my first year of EE. Sem1: Calc 1 & 2, Complex Analysis, Linear Algebra, Boolean Algebra Sem2: Calc 3, Differential equations
Here in Argentina, especially in my University whichever degree you're doing in Calculus II is focused on multivariable calculus as well as Stoke Teorem, divergence or green teorem. However in Calculus III is about Complex Calculus. Never mind i just wanted to share this information.
Yes the course overview he gave is typical of here in the US system. It will vary a great deal even in the US depending on the university and how the department is structured. If your courses are being offered by a university with a strong math research department you will be taught rigor using proofs and such, but a more engineering focused school will hammer on the applied problems and getting solutions for complex and/or unusual situations. At my school I took calculus 1 and 2 from instructors with math degrees, they were heavy on proofs and identities. Calculus 3 I took from a retired aerospace engineer, proofs meant next to nothing to him and the exams were 100% applied problem solving.
Without a deep understanding of the mathematics involved it is really not possible decide how to apply a given software package to obtain a required solution so although you don't tend to do hand calculation much as a professional engineer having a good understanding of the mathematics involved is essential. Also much of the content of an engineering degree course lays the foundation for moving into research where you may well be writing your own software to model a system.
I would say what an engineer sees as “math” is completely different to what a mathematician sees as math. They two completely different worlds. If u think about it, you learn “math” to apply it to the real world, whereas we mathematicians work on a new world with its own rules and develop that new world by creating new theorems and definitions. That is why for us mathematicians, engineering majors teach incredibly limited math and in my opinion I even question that it should be called math. Not trying to sound discouraging but want to be clear and point out the difference. Generally engineers just want to learn “math” that is useful to apply in the real world, so you dont need to understand math fully nor its essence.
@@rubengarciaquismondo Mathematicians tend to specialise in some area of pure maths. Applied mathematics is what engineers are interested in. Engineering is not really coming up with completely new ideas, it is knowing how to apply established technologies and methods to solve problems. All engineers are always mindful that the end result of their endeavours always has to be fully tracible to tested methods and technologies so coming up with your own brand new untested methods is really not useful.
@@schrodingerscat1863 That is correct but the term "deep understanding" is not really suited math for engineers. Not even in the small topics, not even in Calc 1.
@@schrodingerscat1863 I totally agree with you. Im well aware of that, we mathematicians have totally different goals and aren’t interested in real world applications. Its a matter of what you like.
Hey Tamer, your video is awesome! I'd like to add that perhaps Financial Management is "Engineering Economics" in some universities/countries such as here.
I remember taking all of these courses. Been in industry as a computer engineer for almost 30 years, writing engine control system software for much of it. What have I used the most? I would say differential equations and Boolean algebra followed by calculus. The “non-math” course I use the most? Thermodynamics.
I took most of the math courses you mentioned. Another reason you take them--in addition to verify the software results--is to be to UNDERSTAND the results. Thanks for a great video. Good job
In engeniering there is as much math as you want. Every single concept is based or comes from a simplification of a big formula. In collegr you just choose how much of it you wanna learn. If you stay on basis, this video shows what you will learn. Of course in real life you will use only a few percent of that knowledge.
@@rubengarciaquismondo hahahaha this is judging a book by its cover, cant say it in more accurate words. Then by your argument Nikola Tesla was invalid at math?? Hahaha definitely no. I agree with you in the fact that as engineers math is require to understand concept, but we dont work on a day to day basis with it. Anyone can become good at what you call real math if they put the work. I know the math spectrum is very wide, but i know even you as a math person cant cover all of it with the same level of depth.
@@rubengarciaquismondo You shouldn't generalize. Many mathematical transforms from signal processing and methods were actually developed by electrical engineers, see also optimal control.
I majored in biology (now in dental school) but I've always loved math, probably more than the basic sciences. I wish I had the opportunity, throughout undergrad, to explore some of these higher level courses. At the undergraduate level I've taken Calc I and II, statistics (intro), physics I and II... very basic. However, I recall some manipulation problem solving in the upper year organic and inorganic chemistry courses.
@@FreakGUY-007 I agree, but the quality of education matters to me. Direct access to faculty, collaboration with peers, rigid schedule and lecture/exams etc.
@@stevenlopez1717 MIT, NPTEL, and many educators who even surpass some of the professors from MIT are on RUclips.. Many paid courses.. AI which can help and you can debate with... You can make these as rigorous as you want.. Enroll in some paid courses and take tests... Once you put in the money you are now more serious... Tbh learning takes place when you have no rigid schedule and exams... The philosophical aspect can be then understood... And you can publish things if you want. No one stops you... I am in medicine and have studied physics before this for four years... Higher physics is easy for me but it's not because I attended uni... Uni taught me nothing... I bunked classes a lot and studied at home and from online courses.. Just appeared for exams... I used some other means for my attendance... I remember learning about partial derivatives from a book and a video and then understanding thermodynamics.. The uni skipped this chapter as the instructor was busy somewhere else... Everything will be online in the coming years... Collaborations can be done online... I think you are still the old-school type of guy... Even CS degrees from top-rated uni have been started online... You just need to take exams in nearby centers... In my country, online education has increased and quality is not an issue... Many institutions have started online academic programs ( they charge just like offline ) but you can see no difference in quality.. You will be provided with same material and same professors and the same interactive sessions... Now I'm in radiology... I did my postdoc via online mode.. Lol I am learning signal processing... And more abstract subjects... For quality check, I read standard books and solve questions... I can solve them.. Means I know those things.. I even debate with people in the maths and physics community... I am currently working on fluid dynamics of the pathology of CVS..
For my UG course (Mechanical), I had to take-- Calculus, Linear Algebra, Differential & Partial d equations, Statistics, Optimization, Operation Research and Numerical methods, besides special courses for Mechanical. For Graduate course (Transportation) -- Data Analytics, Statistical modeling and Linear Programming. In addition to these, there were a host of Management based Math tools (or shall we say toolkit) which found place in several core courses. Except Humanity based electives, all the courses I've studied had Mathematics of varying difficulty level.
in India, pretty much all the math courses you mentioned are taught within the first two semesters. Differentiation, integration, matrices, and quite a lot of algebra and statistics are already taught during K11 and k12. (We don't have K11 and k12 but a very similar system, where we call it 11th and 12th standards.
@@TamerShaheen complex analysis, courses related to machine design, materials, processes of manufacturing, a whole course on thermal engineering, a course of refrigeration and air conditioning etc.
At my university we have three dedicated math courses called HöMa 1,2 and 3. 1 and 2 are mandatory for every engineering student, the third course has to be taken by mechanical, electrical and automotive engineers. They deal with practically all the concepts you mentioned, though in a far shorter manner. There is a course that deals with FEM and numerical methods, which is one of the hardest courses in the whole engineering program, as cheat sheets aren't allowed and you have to memorize all of the necessary formulas.
I think if you master complicated math, you have some feeling about mastering "difficult things" at all. If you have never mastered anything complicated then problems ahead look much more difficult in general. Doesn't it teach attitude how to think about certain problems? Certainly there are other ways to train that thinking, but I think math would be a very common track to advance problem solving skills.
Did mechanical engineering in Australia, almost all of the stuff you mentioned we did, but most of them were condensed/ combined within applied engineering units. We had two pure math units, the last being a second year advanced mathematics unit which smashed through linear, multivariable calc, matrices, fourier and Laplace in a single half unit. It was the only unit in the degree I dropped out from as I realised I was not ready for the 2nd and 3rd year units. Too many gaps of knowledge. I spent all summer grinding it out, reenrolled and got distinctions and high distinctions all throughout the degree after. I even got to enjoy the most notorious concepts in the course like advanced vibrations, systems and control, fluids ( navier-stokes), etc. If there is one piece of advise I can give, dont skip on the fundamentals or you will spent the rest of the degree memorising steps without actually understanding anything. Most people I've seen doing this, dropped out by 3rd year.
@@krustykrispy5781 i personally havent done a math degree but i could see the synergy. However, i think you might be better off pairing your double with something more practical. The engineering degree will equip you with applied science full of "good enough" math shortcuts and approximation methods, while i hear the mathematics side is a bit more full on. If i had the choice and you go in for the mathematics of it all. I would pair CS with mathematics or do an engineering major involving lots of CS such as CS, Mechatronics or Electrical . There are too many engineers out there scared to code and if you really want to unluck your inner mathematician or engineer you have to learn atleast python.
that was a pretty impressive introduction to " why i had to study so much math in my degree" it explained so well what was the purpose of all the math i did in my degree. i appreciated that your explanation was clear, simple and comprehensive at the same time. so thanks for your effort.
Linear algebra is something used much more frequently than calculus, but I have a hand calculator that will handle most of the heavy lifting. Often times I need to transform from one coordinate system to another. Multiplying a coordinate by a transformation matrix is the best way. But even then, I use a computer to do the heavy lifting.
4th year ME student here, some of those classes you mentioned are not their own course in my university, for example laplace transforms were covered in my diff eq course and linear algebra was taught in my physics and electrical engineering courses to a minimal extent. interesting to see how universities can vary so much in their curriculum
In Spain you have 3 calculus(Calculus I, Calculus II:Algebra and Multivariable and Calculus III: Numerical Calculus. Differential Equations, ) Courses and 1 of Statistics, but in the end is the same, this 4 couses explane all the math taht are explained in this video, laplace, fourier...etc, in my case as an Electric Enginner I learn a lot of fourier, Laplace, matrix calculus and differential ecuations in all the diferent courses of electronics and electric, the math are the only form to solve the problems depending on time and sinusodial waves.
According to me the most difficult part of mathematics is probability theory and stochastic processes...I just can't explain in words the difficulty level.
@@Atistatic Hahah, I broke down laughing and crying when I read this comment! Recently *died* from my course in category theory and homological algebra! Super interesting though I must say, but I will need more time to internalize the concepts.
BSEE in 1976 here. We had Calculus 1, Calculus 2, Multivariable Calculus, Differential Equations, Linear Algebra, Boolean Algebra, Statistics, Discrete Math, Laplace Transforms, Fourier Analysis, Partial Differential Equations, Matrix Theory and Numerical Methods as I recall. We also did a lot of programming-high level, Assembly and bit code-which is considered math study in some respects due to the focus on logical progression. BSEE is the tough one, once you get into the MSEE program you have 'arrived' and are considered to have a math skills sufficient to conduct Engineering Analysis-the Profs start giving you some respect (LOL). PhD is a walk in the park as far as Math formal study, you're breathing rarefied air at that point. Have fun!
Yeah they probably mashed all that down because that would put the studenta beyond the pell grant. My degree itaelf was 144 credits with the transfer inended up graduating woth 150+ credits which disqualified me from Pell. If you decided to go MSEE in telecomm route, the math comes back otherwise ot looked like the embedded/IoT route wasn't as math heavy
For anyone going into Electrical or Computer Eng. all I can say is make sure that Calc 2 and 3 are your best friends cuz your gonna be using that shit non stop. As well as linear algebra lol!
Here's the thing, I can undoubtedly say that all of the skills I have learned thus far have made a genuine difference in the way I approach problems in every day life. The way in which you dissect problems is a crucial skill, it really is the absolute bread and butter of ANY engineering professional. If you lack the ability to work hard enough to break through challenging abstract concepts than how could you possibly provide meaningful input in problems that require optimal solutions? I also find that being able to visualize and truly grasp underlying ideas and truths about the world that you're trying to base your solutions on is invaluable. The math is very doable and is both a mix of providing some meaningful and useful skills but most importantly the mental tools to use in every asset of your life and in providing valuable problem solving skills for your career
I can tell u the mathematical depth in engineering is incredibly low. If you really think you learn abstract thinking in engineering, please do the math major and u will open your eyes.
@@rubengarciaquismondo So here's the thing. I see what you were trying to say but only 4.9% of the entire work force in the united states hold an engineering job. we have to be considerate to the reality that generally speaking engineering mathematics is actually quite challenging for the general population, and it's not hard to see why. it requires an immense amount of investment and interest to tackle. What i'm trying to get it, is that you're absolutely correct that abstract maths is better for what i've mentioned. but, the entire purpose of your engineering specific classes is to tie all the skills together and apply them in a meaningful way, of course specific to whatever you chose to do. to some extent you can't really teach somebody to be proficient at abstraction anyways. it's actually personally what even attracted me to begin with, is that there really is a sort of creativity involved with designing and implementing things. it's the same reason you don't really see colleges for making your own music. anyways theres many takes on it, thats just my personal opinion
We had most of what you showed in Math 1-3. We don`t have financial math, that is something you could choose if you want but most take practical engineering courses or something easy^^. We actually did have statistics in math 3 and some advanced stuff in signals and systems. We also had divergence and curl in simulation theory and recently some stuff about finite fields. I didn`t need to calculate much by hand in practice. But I used a lot of math for optimization problems, especially iterative optimization. It`s quite important to know the basic math behind the models you use. Otherwise, your computer leaves the space of doing something useful and creates something let`s say interesting. I actually needed to dig a bit deeper into algorithms by myself, (FFT) as optimization moved from my desk further and further into the final products themselves.
I'm an industrial engineer and I use probability and statistics all the time. For me statistics and probability were 2 separate courses. Probability was very difficult because it was entirely word problems and actually used quite a bit of concepts from calculus 1 and 2.
Chemical Engineering student here, I just finished my last math course, ready for some of the next courses ahead. I studied Precalculus, it is like calculus without limits, derivatives nor integrals, so basically Algebra for functions. Then Calculus, so the missing stuff from the previous course. Numerical Methods. Probability and Statistics. Differential Equations. And "Advanced Calculus" which was multivariable calculus, with some Linear Algebra at the beginning of the course.
AHAHHAHAHAHAHAHAHA *laughs in fourier tranforms for EE, calc for Classical mechanics, Optics(phones, lightbulbs, etc), probability and stat(physics, statistical thermodynamics, machune learning, etc), Cryptology(Blockchain and Information security/Cybersecurity), Differential equations(growth and decay in physics as well as modeling the groeth of tumors and spread of disease), Real and Complex Analysis (engineering and computer science. Can validate models, helo construct new theorems and understand Calc and Analysis on a deeper level, Topology(has applicationsnin Physics and Matwrials science), Abstract Algebra(Organic chemistry and well as other applictations. Math degrees are highly flexible.
School is school. Work is work. Undergrad curriculum exposes you to concepts that help understand other abstract ideas. In the real world (“industry”), we just need to know enough to keep businesses running. Most of the time, theory/ideas are thrown out in favour of immediate, urgent, “common-sense” solutions and a bunch of existing rules/guidelines. Business is all about making money and jobs serve that function. Unless the business applies abstract Engineering like University/Research institutions do, don’t expect to use any Math.
I used to think the same as you, but trust me, Math its important, even if u dont see an aplication in real world, it will help you to increase your logical level and to think in ways you didnt before
Hey Tamer, enjoy your videos and appreciate your work. When we begin to speak about career/industry experience, it might be a good idea to interview some of your more senior co-workers for further insight. Keep it up!
Im a sheet metal engineer and these comments have me slightly concerned about the absolute lack of math I do on a day to day basis, like outside of typing simple equations into solidworks I do little to none at all.
You’re lucky that your math is divided into so many courses, I’m taking civil engineering program in Sweden and all those courses you mentioned are packed in a maximum of 6 courses whereas the first five courses are taken in the first, second and third semester. The last one comes later on in the program. It is a real pain in the A** to learn all that under that short period of time.
In Belgium in engineering science all of the mentioned subjects plus all of the advanced ones are mandatory for all engineers and is thought in the first 3 semesters lol. The advanced courses based on your specialization after that are super specific and kinda crazy sometimes.
@@cedar4539 I don't know how similar it will be there but honestly I didn't think the math was the hardest part, it's the insane range of topics you have to master for me. Whatever specilization I chose the first year and a half are ton of courses from all science branches and not just some basic course they went advanced (hence the name engineering science). They are also often very very abstract and not very useable yet in you engineering career. I really had to power through these and I often found them uninteresting because they had nothing to do with what I wanted to specialize in. After that year and a half it changes alot though and at that point it starts to make sense. In the end I'm maybe kinda glad it is like that because after graduating my bachelor couple days ago you realise just how much you've learnt about the world around you.
Statistics is incredibly valuable for a Mechanical Engineer. Often times we deal with assemblies with multiple contributors to dimensional variability. Designing to 6 sigma instead of worst possible case will reduce cost dramatically.
It's funny that software does all the heavy lifting, yet software engineering generally requires less math for the degree. I wonder where the extra math is coming from.
I'm studying Indrustrial Engineering in Argentina(UTN), and I've always wondered if the subjets in diferent universities(outside Argentina) have the same learning process or similar classes, this video had confirmed me that all engineers have to suffer the same things, at least in math xd.It's my first year in it, and you mentioned all the things that we are going to study, I'm excited and I'm looking forward to be a great engineer one day! PD: Should I study translation(I can't remenber the name of the degree)after I graduate?
Before watching this vid, I want to answer: Not that much. Although you will see a lot of math in engineering, they are in most case only either linear algebra, basic calculus, prob. theory, diff. Equ
Taking pre calculus rn and have all of those math classes left. I will ace these classes. No point in me typing this comment, just wanted to get my thoughts out there.
My buddy was an Electrical Engineer and he lived and breathed Fourier transforms and knew every trick in the book for MatLab. I went the software engineering route and I'm only barely joking when I say the most complex math I used was adding one to a number - but over and over again ;) I took Calc I, II, and III as well as linear algebra, but I don't remember a single time I used that material outside of the classroom. Boolean algebra and discrete mathematics wove their way through everything of course, but not in ways that were any sort of challenge to work through.
7:33 I would highly highly not agree with you. As an engineer the most important math that you need to understand are numerical methods. With that you can literally discretize and simulate any differential equation system. very useful if you don't have access to a solver like simulink or matlab. Also Newton-Raphson is you friend to resolve so many non-linear constraint problems.... At 9:40, I also don't agree with you, simulation tools are very very very dangerous if you don't understand the math behind it and you don't have a big experimental knowledge. I don't know about mechanical engineering, but I know for certain that in Electrical Engineer once you quit the basic short-circuit software, you need a very deep understanding how of the softwares work.
I study Industrial Engineering in Sweden and the only course of all these courses I have not needed to take is the boolean algebra. Thank you for the video!
Thanks for the video man! It’s very helpful. I’m studying mechanical engineering (fluid mechanics, heat transfer…) and I’m really struggling with Matlab right now. Do you know any good books (with examples and problems) that can help me, please? I’ll be very thankful and good luck 😉
Worked as an electronics engineer for 40 years. Did a lot of motion control. Used laplace transforms and complex algebra constantly throughout my career. Designed circuits and wrote code that performed derivatives, integrals, and filters. Only once did I actually calculate an integral equation, but I had to correlate a theory with data we took.
I’ve used math from every single math class I took in my mechanical engineering degree. It all has really world applications. Don’t fool yourself thinking it has no applications
True. Most engineering students cannot even see how something they learned in the first semester is connected to and used for some more advanced class. So that's why few people can actually figure out how to use math in real life.
I'm a software engineer and I only ever had to go through Calculus II, Calculus III and Linear Algebra were optional as elective courses but there were other
"After you graduate from engineering, you do very little math." I don't remember a single day where I didn't use calculus, complex frequency analysis, or algorithms for EE system design and embedded firmware in wireless SoC 😂
Engineers right out of school typically solve very little math with paper and pencil, but if you climb the ladder, there is a much higher chance of using more advanced mathematics. And it depends wildly on role and field.
As an Aerospace Engineering student, I took almost all of those courses. I just realized I know a lot more math than I thought. Your exposition is awesome.
How much of this do you actually use? Any important advice you can give about the career? Curious and might go into Aerospace.
My advice is to study aerospace engineering only if you are passionate about the aviation/space world. Have a clear vision of what you want to achieve, be it working in your dream company, the job you will have or your future lifestyle. The undergraduate degree is sort of an introduction to all fields of aeronautics. It will be up to you to decide what you're going to specialize in, and how. Doing a master's degree, learning in a company as an intern or on your own. Some students will become aerodynamicists, some structural engineers, some materials engineers, control systems engineers, airport engineers, etc. Get my point? When you specialize, you will work with only a few of the things you will have learned in college, but all of them will be somehow connected in the company. It's not about how much math you will use in your working life, but that you need to have mathematical tools for all possible applications in the aeronautical world. In real life, as Tamer says, a computer will take care of calculations. I shall add that you learn math in order to train your mind and prove you can put in the work. Take care and be passionate!
@@aiero-h2x Thank you so much, I really needed this.
@@aiero-h2x - thank you!
@@aiero-h2x thanks!
I thought my master's degree didn't involve that much math, because I am a medical engineer. But after watching the video, I noticed that I've completed about 80% of what you mentioned.
Does medical engineering actually use math ?
Like.... just a few math in there right ?
I think it's full of theory 😅
@@tienhung3112 We use actually a lot of math, because we are working with fluidic models, biomechanic forces, differential equations for dynamic systems, complex numbers for electrical engineering, fourier transform for MRT reconstruction & spectra. It's also quite important to get the models into programmed applications.
I’ve never heard of a medical engineer what is that?
@@realdotty5356 Medical engineering is an interdisciplinary study program with focus on mechanical, electrical engineering and informatics combined with medical contents. Typical fields for work are medical imaging for MRI/CT scans, active and passive implants and other hospital-/laboratory devices.
As a graduate engineer, I can say, core material of math classes are for building the way of thinking and perspective which can incredibly useful in advanced degree and professional life.
Understanding the underlying problems will help you think about things that happen when you make higher level actions. Which is way more important to engineering then anything else.
Agreed
So is this engineering copium?
@@YuTEM yes, this literally applies to anything, look at medicine, a substance can treat a symptom but if you don't treat the cause of the symptom are you really treating the person? Or music, when writing a song you don't just look at "the next 3 notes" a good song feels complete if it all works together, or mathematics, focusing on solving just a single specific problem isn't very useful, the usefulness comes form understanding the general solution to the general problem, and so on...
@@zirkereuler5242 'mkay
As a mathematician, I must say I don't use these classes very often either, but what I absolutely value from them is their significance in the development of my problem solving skills, which at the end of the day is what we (engineers and mathematicians alike) essentially are, is problem solvers.
do you work as a mathematician? or some math heavy job like Data analyst?
The point of certain algorithms is to know which one to use and understand
A statistician can know normal distribution best but what happens when the model cannot be approximated by normal distribution? You need to either design your own distribution or understand that the model fits something else instead. But notice you’re not expected to compute out everything (mean, median, std dev) the computer will do that for you but your numbers are meaningless if you compute with normal instead of the more accurate model
A problem solver! That’s what i will learn to be.
what can a math graduate worke ?
I'm literally overwhelmed with my classes today this is what I needed to hear.
As someone who has taken calc 1, 2, 3, differential equations, and linear algebra, and is going into my junior year of aerospace engineering, I can say that I haven’t taken a single class in my major that didn’t involve math, including calculus. Math is used all the time in school for engineering and we use Matlab in all lab courses. Math is definitely a crucial part of engineering and in my opinion makes it more fun! Math can be very useful in industry for doing hand calculations and for checking code, but often times math is done by computer programs such as ANSYS or Matlab. However, it’s still important to understand the fundamentals of where everything comes from, which requires all levels of calculus.
But how much of that is used in your actual job tho. Like %
@@jayevans6146 I have yet to get a real engineering job, so I can’t give you an accurate answer. I did an internship though and the engineers used math and calculus to verify that their code was working properly. As the video states, many types of software exists to help with engineering, but it is definitely useful to know the science and math behind the software to verify that it works properly.
@@infinitespace8313 It was mostly rhetorical. I already know.
In reality, about 5%-10% of your actual job will involve actual higher level math/Cal DEs etc
@@jayevans6146 but even then if you didn't learn about those higher level math in school then you wouldn't know it in industry. Even if something constitutes only 1% of your job, you should still be learning of what it is and how it works rather than not knowing it. Of course there is the obvious time investment as these higher level classes take much longer to learn due to their difficulty, but even so if it is used in the field no matter how miniscule you should still learn it in school
@@jayevans6146 Not every engineering field is the same, aerospace is one of the strongest if not the strongest math related engineering, biotech, nano, biomedical, systems, industrial engineers may not need the same amount of math than aerospace
Engineering school doesn't give you every tool you need but it fills your box up with a lot of tools and ways to think about the world. You need the math to really be able to apply concepts in a broad sense. In my field, I use a ton of heavy math. I learned a large part of my math and numerical analysis skills in engineering school. You are also learning different thought paradigms as some others have mentioned, and a rigorous mathematics education is essential to those paradigms.
In Italy calc 1 and 2 are one single exam, just called calculus 1, and calc 3 is called calculus 2 which also includes Differential Equations
Yes. I also noticed that in the American system one can enter a PHD program with only a bachelors and sufficient research experience, whereas for England, and I presume also italy, one must have a masters before being admitted into the PHD. Is this true of Italy?
who asked?
@@randallmcgrath9345 This is true in America, but the PhD program is usually longer, and would be almost equal to getting your master's along the way. Having your master's and then getting a PhD is probably still the more popular route in the US and of similar length in the grand scheme of graduate studies.
@@maxwellwallace8553 I was about to say this! Well put.
@REPUBBLICA ITALIANA ma dici sul serio?
As an electronic engineering student who has also studied mechanical engineering before, I can't believe that I learned everything mentioned...
A great overview. I found engineering maths very difficult, but luckily the real world was much more software and ‘Pilot/POC’ based. That’s partly because the simplifications needed to make mathematical models work don’t give reliable answers. I saw this from stress analysis for rocket design (where FEA was used) to avionic circuit design.
Having said that engineering is all about learning to problem solve and learning to learn, and engineering maths trains you in both. All problems I’ve ever solved seem less confronting than solving a second order non-linear differential equation!
Ironically the number one job most engineers quickly find themselves in is leading teams and dealing with people, something many engineering degrees ignore!
I found out about the last part later on. I've warmed up to team and project management but it was difficult at first because I'm not a people person.
We had both differential and integral calculus in one semester and calculus 2 was already multivariable calculus. But instead of being called calculus it was called mathematics for applied sciences, because the class actually called calculus was too pure for applied sciences majors. I'm a CS major and I think around half of our classes are math.
Thanks for sharing and that makes sense. Computer science majors at my school were under the faculty of mathematics…so it makes sense that there’s so much math involved in CS.
was this in the US, if so, did you touch deep into integration methods and applications in one semester?
I attest to that. I'm CS major also in Africa ghana. Ours is 80%. Less programming, more math and physics
That's an interesting setup. Where is the school?
A prof in alexanderia U once said, not all math have been you studied in the university you will use it, you just need few basic topics, but studying math build your muscles to "understand anything tough" 💪💪
The only thing that the math serves for engineers is that there is an appreciation that the models you are using in simulation are reasonably approximated. It is near universal that math in your every day engineering job doesn't really go much farther than some basic algebra and trigonometry. We appreciate the math majors and engineers that work together that make the CAD software a reality which helps everybody else's jobs become much easier.
It's not only that. You also need people to build the software to begin with. I worked in civil engineering in a firm where we did A LOT of in-house model building. So yeah, the math was used frequently when building the tools. Less when using them.
as a civil engineer on my 4th year, I realized I was mostly doing the basic algebra math's, very few calculus or non at all around the 3/4 years so it kind of depends on your major, if you choose mechanical u might have to apply more calculus equations and stuff along with algebra so yeah.
So is this the easiest one ?
Nothings ez my guy
Engineering is strange in the fact that you can skate by a whole degree without fully understanding derivations of the equations as long as you know how to apply them. However, if you want a deeper understanding it is very essential you try to understand the foundations on which the concepts were built aka the mathematics. Then you will be able to understand the engineering concept in its entirety which will help guide decision making in later engineering problems.
What subject teaches the foundations?
@@12degreesnowman11 If you master calculus 1/2, physics, and differential equations you will have the best intuition when you get to the applied classes.
@@12degreesnowman11 Start with Real Analysis.
@@stevemenegaz9824 do you have any books to recommend?
@@12degreesnowman11 DId my reply show up?
Thank you so much for this. I really couldn't find a succinct video to cover this and you showed it all in great simplicity.
As a 3rd year CompE major, this video is pretty accurate. Nice well researched video! Love that you’re so knowledgeable about many majors and fields
6:50 as a math purist it's rather about i^2 = -1 because the square root is a function with a positive real domain
In complex analysis the square root can be defined as a two-valued relation so i = \sqrt{-1} is correct ( i is the image of 1 in the principal branch)
@@santiago_moralesduarte The complex number system is a field and for that, at the introductory level, the definition i=\sqrt{-1} is really a very poor definition. Nice for high school level, not for serious college level. I vehemently agree with Abdusselam and that's how we learned it too. In fact, our notation was (0,1)x(0,1)=(-1,0)
i like your funny words magic man
I remember when I studied signal and systems, I feel very good about the Fourier series and the math, but I feel it was pretty tricky later on to a class called communication system, which introduce a lot of digital modulation theories. And after this, we have DSP, which is even harder than signal and system
I’m a Chem E and my father is a mechanical engineer, he despises the younger generation of engineers, from his point of view none of them can do the math off the top of their heads or complete drawings without computer assistance. I’ll admit he’s old, like real old lol! But he kind of has a point. For lot of these kids coming through the pipeline I’m personally not confident in their abilities to perform on the job, even after a couple years of training they aren’t up to standards enough to take on larger projects, it’s like they get comfortable in their niche and they stay there and the curiosity about the job just falls off. Every so often there’s one or two rockstars that come out of college but at the rate society is going, every year university standards drop further and further to the point that I really do worry about the future of the career field over all in every discipline. Universities really should re-up the rigor because it’s causing a quality issue to some extent.
A lot of these topics weren't even courses in my college, we just learned about them when we needed them like laplace transform in circuit analysis, and fourier series in intro to signal processing
What a fantastic channel! As an engineering student, i simply love your content, keep it up!
Hey great video, mechanical engineer here with some additions:
Fourier analysis actually is also quite important for mechanical engineering, namely vibrations. Vibrations can cause materials to fatigue, it can be used to monitor the structural health of e.g. bridges (lower stiffness of beams result in a shifting eigenfrequency), vibrations can be countered using Fourier analysis (see the Bambu lab x1 carbon 3D printer, which has active vibration control). It is also important for mathematically modeling systems. Here I am only touching the surface of how much practical use there is for vibrations. It is a technical field on it own really.
Calculus 3 does have its practical use. It comes back in fluid dynamics, gravity fields, aerodynamics, electromechanics. E.g. vector fields can describe the flow of a fluid or the effect of gravity on a object moving through space.
Hope that helps.
Thanks a lot man. Got a bird eye view of my Engineering career path
This is a good video. Well put together and excellent information.
I have a lot of introductory engineer students taking the Calculus sequence. Not all students are that good in math and some complain why they need all that math. And then a bit later there is this field called fluid dynamics...oh yeah baby!
It is not that hard unless you are the one who is doing the proofing
Crazy how different it is in Belgium, computer engineering is more like a mix of computer science and engineering here. Calc 2 is named calc 1 here and it included ODE's and series, calc 2 is multivariable analysis and calc 3 is vector analysis, PDE's and a bit of complex analysis. All engineering majors have to take statistics, discrete math intro and probability. As a CS/E student I have a lot of courses which include fourier and laplace transforms and z transforms such as signal processing, deterministic and stochastic signals and systems. And of course a lot of boolean algebra in courses like digital electronics and discrete mathematics.
Here in Brazil I'm seeing boolean algebra in digital eletronics as well.
Frankly it's just about the same.
Math really rules the world of Engineering for a bright present and the future.
Greetings from Brazil. I studied everything mentioned in the video. And indeed, after graduating from college, I've rarely studied all the complex math I learned in college. Currently I work on the power distribution system. In the future I intend to go into projects, where I will be able to apply more of the engineering I learned.
I have been an electronics engineer for about 20 years and I can say Physics and applied math is the most important. Things like finding out how to setup a timer register in a microcontroller or doing a conversion from a A/D converter to a value that means something example(temperature) is majority of the math I use. Finding out how much power is needed and how thick the traces on the circuit board needs to be, are other examples of applied math i have used. I think sometimes colleges over emphasize math and it can scare people away from engineering. Creativity, problem solving, and being able to take an idea to a product is more important. Saying that, being exposed to different math ideas is also useful, but you do not need to be an expert. At the end of the day in the real world, what matters is how good you are at solving a problem and coming up with an idea and able to take that idea and use it.
best mech eng youtuber ever. so much valuable information. thanks a lot 🙏.
haha appreciate that :)
Probably should mention about how complex analysis is fundamental to field theories - as the conformal mapping and superimposition allows all sorts of analysis (eg inviscid and incompressible flows and EM field)
In Germany we have nearly all of these math concepts included in three courses, called Higher Math 1, 2 and 3, which you have to do in the first three semesters of your studies.
Also I can say, that you need most of these math concepts in later courses to describe and calculate with the formulas in the given topic. Especially differential equation will pop up everywhere. So it is kind of helpful to learn all of that in the beginning and than apply that in later courses.
So if you wanna go into research it's quite helpful to understand the underlying math of the equations and formulas you are working with.
Great vids! It's fun to hear about the experience of engineering students from other countries.
Same for me, (Also from Germany)but partial differential equations is in the Master studies of EE. We’ve have a module there called higher maths.
Hatte bis jetzt analayis 1,2, lineare algebra und gewöhnliche DGL. Bin aber erst immer zweiten Semester
@@samuellandos785 which city are u in university? Munich, Duisburg , Essen or what? cause I heard Munich is the hardest
@@samuellandos785 Bei euch ist das heutzutage sowieso alles anders. Als ich studiert habe (Ende der Diplom-Ära) hieß das alles anders, war extrem konzentriert in wenige Vorlesungen und Prüfungen, und reichte *viel* weiter als bei euch heutzutage. Im Ingenieurwesen wurde in den letzten 15-20 Jahren so einiges an mathematischem und physikalischem Tiefgang gestrichen bzw. als Wahlpflicht ausgegliedert. Auf der anderen Seite werdet ihr aber auch extrem gegängelt. Bei mir gab es noch etwas, das hieß "Grundstudium" und ich mußte Scheine machen. Wortwörtlich Scheine. Zettel. Analoges Papier ;-)
Die hat man ausgestellt bekommen, wie Akten fakturiert, und irgendwann als Stapel der ollen häßlichen Zicke im Prüfungsamt auf den Tisch gelegt, um zu den Klausuren der Diplom-Vorprüfung zugelassen zu werden. Wenn man das Grundstudium geschafft hatte, wiederholte sich dieses unverschulte, unbegleitete, frei vom Studenten zu gestaltende Verfahren bis zur Ablegung der Diplom-Hauptprüfung. Die Noten des Grundstudiums wurden nie wieder gesehen. Die Endnote berechnete sich nur aus den Prüfungsteilen des Hauptstudiums.
@@bobbwc7011 Das ist so typisches früher war alles besser Gelaber. Beweise doch dass es früher tiefer ging als heute mal abgesehen dass das vom Standort abhängt. Es ist eigentlich eher umgekehrt. Heute werden die Grundlagen aller fachähnlichen Diplomstudiengänge in ein Bachelorstudium gepfercht.
I have spent most of my life working with patents, largely in the area of communications, and most recently in artificial intelligence. I cannot begin to emphasize how important a good, solid understanding of advanced mathematics has been to me.
What I find very interesting is that a lot of these courses are mashed together at the university where I study. Calculus I and II are Higher Mathematics I, linear algebra is Higher Mathematics II and Calculus III, differential equations and partial differential equations is Higher Mathematics III for example
I’m going to use this video as a check list. I just finished my first year of EE.
Sem1: Calc 1 & 2, Complex Analysis, Linear Algebra, Boolean Algebra
Sem2: Calc 3, Differential equations
How’s it going now ?
@@Amrgoated Currently (Sem3) on Stochastics, Fourier Transform, complex functions and even more differntial equations!
Here in Argentina, especially in my University whichever degree you're doing in Calculus II is focused on multivariable calculus as well as Stoke Teorem, divergence or green teorem. However in Calculus III is about Complex Calculus. Never mind i just wanted to share this information.
Yes the course overview he gave is typical of here in the US system. It will vary a great deal even in the US depending on the university and how the department is structured. If your courses are being offered by a university with a strong math research department you will be taught rigor using proofs and such, but a more engineering focused school will hammer on the applied problems and getting solutions for complex and/or unusual situations.
At my school I took calculus 1 and 2 from instructors with math degrees, they were heavy on proofs and identities. Calculus 3 I took from a retired aerospace engineer, proofs meant next to nothing to him and the exams were 100% applied problem solving.
Without a deep understanding of the mathematics involved it is really not possible decide how to apply a given software package to obtain a required solution so although you don't tend to do hand calculation much as a professional engineer having a good understanding of the mathematics involved is essential. Also much of the content of an engineering degree course lays the foundation for moving into research where you may well be writing your own software to model a system.
I enjoyed reading this comment and its insight.
I would say what an engineer sees as “math” is completely different to what a mathematician sees as math. They two completely different worlds. If u think about it, you learn “math” to apply it to the real world, whereas we mathematicians work on a new world with its own rules and develop that new world by creating new theorems and definitions. That is why for us mathematicians, engineering majors teach incredibly limited math and in my opinion I even question that it should be called math. Not trying to sound discouraging but want to be clear and point out the difference. Generally engineers just want to learn “math” that is useful to apply in the real world, so you dont need to understand math fully nor its essence.
@@rubengarciaquismondo Mathematicians tend to specialise in some area of pure maths. Applied mathematics is what engineers are interested in. Engineering is not really coming up with completely new ideas, it is knowing how to apply established technologies and methods to solve problems. All engineers are always mindful that the end result of their endeavours always has to be fully tracible to tested methods and technologies so coming up with your own brand new untested methods is really not useful.
@@schrodingerscat1863 That is correct but the term "deep understanding" is not really suited math for engineers. Not even in the small topics, not even in Calc 1.
@@schrodingerscat1863 I totally agree with you. Im well aware of that, we mathematicians have totally different goals and aren’t interested in real world applications. Its a matter of what you like.
Hey Tamer, your video is awesome!
I'd like to add that perhaps Financial Management is "Engineering Economics" in some universities/countries such as here.
That was a really good summary description. Thank you
I remember taking all of these courses. Been in industry as a computer engineer for almost 30 years, writing engine control system software for much of it. What have I used the most? I would say differential equations and Boolean algebra followed by calculus. The “non-math” course I use the most? Thermodynamics.
I took most of the math courses you mentioned. Another reason you take them--in addition to verify the software results--is to be to UNDERSTAND the results. Thanks for a great video. Good job
In engeniering there is as much math as you want. Every single concept is based or comes from a simplification of a big formula. In collegr you just choose how much of it you wanna learn. If you stay on basis, this video shows what you will learn. Of course in real life you will use only a few percent of that knowledge.
Someone needs to make the simulation software too you know?
Engineers have no idea about math, not even its essence (i am a mathematician)
@@rubengarciaquismondo hahahaha this is judging a book by its cover, cant say it in more accurate words. Then by your argument Nikola Tesla was invalid at math?? Hahaha definitely no. I agree with you in the fact that as engineers math is require to understand concept, but we dont work on a day to day basis with it. Anyone can become good at what you call real math if they put the work. I know the math spectrum is very wide, but i know even you as a math person cant cover all of it with the same level of depth.
@@rubengarciaquismondo You shouldn't generalize. Many mathematical transforms from signal processing and methods were actually developed by electrical engineers, see also optimal control.
@@anders5611Yes people like me (master physics), make this stuff.
I majored in biology (now in dental school) but I've always loved math, probably more than the basic sciences. I wish I had the opportunity, throughout undergrad, to explore some of these higher level courses.
At the undergraduate level I've taken Calc I and II, statistics (intro), physics I and II... very basic. However, I recall some manipulation problem solving in the upper year organic and inorganic chemistry courses.
Everything available online.. You don't need to get into a uni to learn maths..
@@FreakGUY-007 I agree, but the quality of education matters to me. Direct access to faculty, collaboration with peers, rigid schedule and lecture/exams etc.
@@stevenlopez1717 MIT, NPTEL, and many educators who even surpass some of the professors from MIT are on RUclips.. Many paid courses.. AI which can help and you can debate with...
You can make these as rigorous as you want.. Enroll in some paid courses and take tests... Once you put in the money you are now more serious...
Tbh learning takes place when you have no rigid schedule and exams... The philosophical aspect can be then understood... And you can publish things if you want. No one stops you... I am in medicine and have studied physics before this for four years...
Higher physics is easy for me but it's not because I attended uni... Uni taught me nothing... I bunked classes a lot and studied at home and from online courses.. Just appeared for exams...
I used some other means for my attendance... I remember learning about partial derivatives from a book and a video and then understanding thermodynamics.. The uni skipped this chapter as the instructor was busy somewhere else...
Everything will be online in the coming years... Collaborations can be done online... I think you are still the old-school type of guy... Even CS degrees from top-rated uni have been started online... You just need to take exams in nearby centers... In my country, online education has increased and quality is not an issue... Many institutions have started online academic programs ( they charge just like offline ) but you can see no difference in quality.. You will be provided with same material and same professors and the same interactive sessions...
Now I'm in radiology... I did my postdoc via online mode.. Lol
I am learning signal processing... And more abstract subjects... For quality check, I read standard books and solve questions... I can solve them.. Means I know those things.. I even debate with people in the maths and physics community... I am currently working on fluid dynamics of the pathology of CVS..
For my UG course (Mechanical), I had to take-- Calculus, Linear Algebra, Differential & Partial d equations, Statistics, Optimization, Operation Research and Numerical methods, besides special courses for Mechanical.
For Graduate course (Transportation) -- Data Analytics, Statistical modeling and Linear Programming. In addition to these, there were a host of Management based Math tools (or shall we say toolkit) which found place in several core courses.
Except Humanity based electives, all the courses I've studied had Mathematics of varying difficulty level.
I love this video so much, a lot of info and it's all very too the point and wastes no time, great video and thanks for the info
in India, pretty much all the math courses you mentioned are taught within the first two semesters. Differentiation, integration, matrices, and quite a lot of algebra and statistics are already taught during K11 and k12. (We don't have K11 and k12 but a very similar system, where we call it 11th and 12th standards.
Oh damn that’s crazy, so what more math do you do in the later semesters if you already did everything in the first two semesters?
@@TamerShaheen complex analysis, courses related to machine design, materials, processes of manufacturing, a whole course on thermal engineering, a course of refrigeration and air conditioning etc.
Tyre engineering, internal combustion engines.
@@bhupendrakumar2520 it explains why people from India are the best in IT
@@ArmanZharas And get paid the least ngl
At my university we have three dedicated math courses called HöMa 1,2 and 3. 1 and 2 are mandatory for every engineering student, the third course has to be taken by mechanical, electrical and automotive engineers. They deal with practically all the concepts you mentioned, though in a far shorter manner. There is a course that deals with FEM and numerical methods, which is one of the hardest courses in the whole engineering program, as cheat sheets aren't allowed and you have to memorize all of the necessary formulas.
I think if you master complicated math, you have some feeling about mastering "difficult things" at all.
If you have never mastered anything complicated then problems ahead look much more difficult in general.
Doesn't it teach attitude how to think about certain problems?
Certainly there are other ways to train that thinking, but I think math would be a very common track to advance problem solving skills.
In civil engineering practice, we do a page or two of advanced arithmetic, then argue with lawyers for a year or two.
Did mechanical engineering in Australia, almost all of the stuff you mentioned we did, but most of them were condensed/ combined within applied engineering units. We had two pure math units, the last being a second year advanced mathematics unit which smashed through linear, multivariable calc, matrices, fourier and Laplace in a single half unit. It was the only unit in the degree I dropped out from as I realised I was not ready for the 2nd and 3rd year units. Too many gaps of knowledge. I spent all summer grinding it out, reenrolled and got distinctions and high distinctions all throughout the degree after. I even got to enjoy the most notorious concepts in the course like advanced vibrations, systems and control, fluids ( navier-stokes), etc.
If there is one piece of advise I can give, dont skip on the fundamentals or you will spent the rest of the degree memorising steps without actually understanding anything. Most people I've seen doing this, dropped out by 3rd year.
Would you say it's a good idea to double major in engineering and mathematics?
@@krustykrispy5781 i personally havent done a math degree but i could see the synergy. However, i think you might be better off pairing your double with something more practical. The engineering degree will equip you with applied science full of "good enough" math shortcuts and approximation methods, while i hear the mathematics side is a bit more full on.
If i had the choice and you go in for the mathematics of it all. I would pair CS with mathematics or do an engineering major involving lots of CS such as CS, Mechatronics or Electrical .
There are too many engineers out there scared to code and if you really want to unluck your inner mathematician or engineer you have to learn atleast python.
that was a pretty impressive introduction to " why i had to study so much math in my degree"
it explained so well what was the purpose of all the math i did in my degree. i appreciated that your explanation was clear, simple and comprehensive at the same time. so thanks for your effort.
Linear algebra is something used much more frequently than calculus, but I have a hand calculator that will handle most of the heavy lifting. Often times I need to transform from one coordinate system to another. Multiplying a coordinate by a transformation matrix is the best way. But even then, I use a computer to do the heavy lifting.
I'm in the last engineer year and I realized that this video is excellent, All the maths as you have to learn to be a engineer are here!
4th year ME student here, some of those classes you mentioned are not their own course in my university, for example laplace transforms were covered in my diff eq course and linear algebra was taught in my physics and electrical engineering courses to a minimal extent. interesting to see how universities can vary so much in their curriculum
In Spain you have 3 calculus(Calculus I, Calculus II:Algebra and Multivariable and Calculus III: Numerical Calculus. Differential Equations, ) Courses and 1 of Statistics, but in the end is the same, this 4 couses explane all the math taht are explained in this video, laplace, fourier...etc, in my case as an Electric Enginner I learn a lot of fourier, Laplace, matrix calculus and differential ecuations in
all the diferent courses of electronics and electric, the math are the only form to solve the problems depending on time and sinusodial waves.
According to me the most difficult part of mathematics is probability theory and stochastic processes...I just can't explain in words the difficulty level.
Probably because it involves a lot of differentiation an abstract thinking
That's cuz you don't know about category theory, homological algebra or maybe number theory.
@@Atistatic Hahah, I broke down laughing and crying when I read this comment! Recently *died* from my course in category theory and homological algebra! Super interesting though I must say, but I will need more time to internalize the concepts.
@@jacobskarby1389 surely that does take time. Even more than you need internalize abstract algebra for the first time.
Ok
BSEE in 1976 here. We had Calculus 1, Calculus 2, Multivariable Calculus, Differential Equations, Linear Algebra, Boolean Algebra, Statistics, Discrete Math, Laplace Transforms, Fourier Analysis, Partial Differential Equations, Matrix Theory and Numerical Methods as I recall. We also did a lot of programming-high level, Assembly and bit code-which is considered math study in some respects due to the focus on logical progression. BSEE is the tough one, once you get into the MSEE program you have 'arrived' and are considered to have a math skills sufficient to conduct Engineering Analysis-the Profs start giving you some respect (LOL). PhD is a walk in the park as far as Math formal study, you're breathing rarefied air at that point. Have fun!
Yeah they probably mashed all that down because that would put the studenta beyond the pell grant. My degree itaelf was 144 credits with the transfer inended up graduating woth 150+ credits which disqualified me from Pell.
If you decided to go MSEE in telecomm route, the math comes back otherwise ot looked like the embedded/IoT route wasn't as math heavy
For anyone going into Electrical or Computer Eng. all I can say is make sure that Calc 2 and 3 are your best friends cuz your gonna be using that shit non stop. As well as linear algebra lol!
Here's the thing, I can undoubtedly say that all of the skills I have learned thus far have made a genuine difference in the way I approach problems in every day life. The way in which you dissect problems is a crucial skill, it really is the absolute bread and butter of ANY engineering professional. If you lack the ability to work hard enough to break through challenging abstract concepts than how could you possibly provide meaningful input in problems that require optimal solutions? I also find that being able to visualize and truly grasp underlying ideas and truths about the world that you're trying to base your solutions on is invaluable. The math is very doable and is both a mix of providing some meaningful and useful skills but most importantly the mental tools to use in every asset of your life and in providing valuable problem solving skills for your career
I can tell u the mathematical depth in engineering is incredibly low. If you really think you learn abstract thinking in engineering, please do the math major and u will open your eyes.
@@rubengarciaquismondo So here's the thing. I see what you were trying to say but only 4.9% of the entire work force in the united states hold an engineering job. we have to be considerate to the reality that generally speaking engineering mathematics is actually quite challenging for the general population, and it's not hard to see why. it requires an immense amount of investment and interest to tackle. What i'm trying to get it, is that you're absolutely correct that abstract maths is better for what i've mentioned. but, the entire purpose of your engineering specific classes is to tie all the skills together and apply them in a meaningful way, of course specific to whatever you chose to do. to some extent you can't really teach somebody to be proficient at abstraction anyways. it's actually personally what even attracted me to begin with, is that there really is a sort of creativity involved with designing and implementing things. it's the same reason you don't really see colleges for making your own music. anyways theres many takes on it, thats just my personal opinion
We had most of what you showed in Math 1-3. We don`t have financial math, that is something you could choose if you want but most take practical engineering courses or something easy^^.
We actually did have statistics in math 3 and some advanced stuff in signals and systems. We also had divergence and curl in simulation theory and recently some stuff about finite fields.
I didn`t need to calculate much by hand in practice. But I used a lot of math for optimization problems, especially iterative optimization. It`s quite important to know the basic math behind the models you use. Otherwise, your computer leaves the space of doing something useful and creates something let`s say interesting.
I actually needed to dig a bit deeper into algorithms by myself, (FFT) as optimization moved from my desk further and further into the final products themselves.
I'm an industrial engineer and I use probability and statistics all the time. For me statistics and probability were 2 separate courses. Probability was very difficult because it was entirely word problems and actually used quite a bit of concepts from calculus 1 and 2.
The beeeeeest video I've founddd, *cries in math*
I watched this video 3 years ago, and now I'm in my 2nd year of engineering, thank you so much
Thanks 🙏, Really useful for High Schoolers
Chemical Engineering student here, I just finished my last math course, ready for some of the next courses ahead.
I studied Precalculus, it is like calculus without limits, derivatives nor integrals, so basically Algebra for functions.
Then Calculus, so the missing stuff from the previous course.
Numerical Methods.
Probability and Statistics.
Differential Equations.
And "Advanced Calculus" which was multivariable calculus, with some Linear Algebra at the beginning of the course.
This is why I'm aiming for research or doing software for engineering. It doesn't make sense to me to learn all of that Math only to not use it
Trust me.. u will need
Pretty sure every degree that have "engineering" in it will learn these maths
AHAHHAHAHAHAHAHAHA *laughs in fourier tranforms for EE, calc for Classical mechanics, Optics(phones, lightbulbs, etc), probability and stat(physics, statistical thermodynamics, machune learning, etc), Cryptology(Blockchain and Information security/Cybersecurity), Differential equations(growth and decay in physics as well as modeling the groeth of tumors and spread of disease), Real and Complex Analysis (engineering and computer science. Can validate models, helo construct new theorems and understand Calc and Analysis on a deeper level, Topology(has applicationsnin Physics and Matwrials science), Abstract Algebra(Organic chemistry and well as other applictations. Math degrees are highly flexible.
School is school. Work is work.
Undergrad curriculum exposes you to concepts that help understand other abstract ideas.
In the real world (“industry”), we just need to know enough to keep businesses running. Most of the time, theory/ideas are thrown out in favour of immediate, urgent, “common-sense” solutions and a bunch of existing rules/guidelines. Business is all about making money and jobs serve that function. Unless the business applies abstract Engineering like University/Research institutions do, don’t expect to use any Math.
I used to think the same as you, but trust me, Math its important, even if u dont see an aplication in real world, it will help you to increase your logical level and to think in ways you didnt before
Hey Tamer, enjoy your videos and appreciate your work. When we begin to speak about career/industry experience, it might be a good idea to interview some of your more senior co-workers for further insight. Keep it up!
Im a sheet metal engineer and these comments have me slightly concerned about the absolute lack of math I do on a day to day basis, like outside of typing simple equations into solidworks I do little to none at all.
U present all these courses in a splendid way.
You’re lucky that your math is divided into so many courses, I’m taking civil engineering program in Sweden and all those courses you mentioned are packed in a maximum of 6 courses whereas the first five courses are taken in the first, second and third semester. The last one comes later on in the program. It is a real pain in the A** to learn all that under that short period of time.
Which semester are you in?
@@SH-mz6ec I am on third year which is the fifth semester.
@@HN-vu8pp great👌
I am the second semester civil engineering student.
I am so worried about how to study. Because many lessons are difficult
@@SH-mz6ecWhich country are you studying in? Yes it gets difficult, but if you put in more hours of work things tends to get easier.
@@HN-vu8pp
I am student in Afghanistan
After seeing the video I can say that engineering would be interesting. As I love math & the name of the courses fascinates me too much.
In Belgium in engineering science all of the mentioned subjects plus all of the advanced ones are mandatory for all engineers and is thought in the first 3 semesters lol. The advanced courses based on your specialization after that are super specific and kinda crazy sometimes.
@@cedar4539 I don't know how similar it will be there but honestly I didn't think the math was the hardest part, it's the insane range of topics you have to master for me. Whatever specilization I chose the first year and a half are ton of courses from all science branches and not just some basic course they went advanced (hence the name engineering science). They are also often very very abstract and not very useable yet in you engineering career. I really had to power through these and I often found them uninteresting because they had nothing to do with what I wanted to specialize in. After that year and a half it changes alot though and at that point it starts to make sense. In the end I'm maybe kinda glad it is like that because after graduating my bachelor couple days ago you realise just how much you've learnt about the world around you.
Statistics is incredibly valuable for a Mechanical Engineer. Often times we deal with assemblies with multiple contributors to dimensional variability. Designing to 6 sigma instead of worst possible case will reduce cost dramatically.
It's funny that software does all the heavy lifting, yet software engineering generally requires less math for the degree. I wonder where the extra math is coming from.
Computer science
Nice video! Thank god this video and this channel appeared in my home feed! Nice video!
I'm studying Indrustrial Engineering in Argentina(UTN), and I've always wondered if the subjets in diferent universities(outside Argentina) have the same learning process or similar classes, this video had confirmed me that all engineers have to suffer the same things, at least in math xd.It's my first year in it, and you mentioned all the things that we are going to study, I'm excited and I'm looking forward to be a great engineer one day!
PD: Should I study translation(I can't remenber the name of the degree)after I graduate?
Me too ❤️
Amazing, amazing. If I was to be sincere with you, I only got to understand the purpose of all these maths I've learnt in this video. cheers man
Before watching this vid, I want to answer: Not that much. Although you will see a lot of math in engineering, they are in most case only either linear algebra, basic calculus, prob. theory, diff. Equ
An outstanding explanation sir...,Warm greetings from The Netherlands (Europe)
Taking pre calculus rn and have all of those math classes left. I will ace these classes. No point in me typing this comment, just wanted to get my thoughts out there.
You got this bro!!
Good luck
My buddy was an Electrical Engineer and he lived and breathed Fourier transforms and knew every trick in the book for MatLab. I went the software engineering route and I'm only barely joking when I say the most complex math I used was adding one to a number - but over and over again ;) I took Calc I, II, and III as well as linear algebra, but I don't remember a single time I used that material outside of the classroom. Boolean algebra and discrete mathematics wove their way through everything of course, but not in ways that were any sort of challenge to work through.
I'm almost done with my third year of electrical engineering and I've taken all the courses that you mentioned in this video
Very informative I studies maths till high school and changed faculty to management science but it's so nice the way you explained it
7:33 I would highly highly not agree with you. As an engineer the most important math that you need to understand are numerical methods. With that you can literally discretize and simulate any differential equation system. very useful if you don't have access to a solver like simulink or matlab. Also Newton-Raphson is you friend to resolve so many non-linear constraint problems.... At 9:40, I also don't agree with you, simulation tools are very very very dangerous if you don't understand the math behind it and you don't have a big experimental knowledge. I don't know about mechanical engineering, but I know for certain that in Electrical Engineer once you quit the basic short-circuit software, you need a very deep understanding how of the softwares work.
I study Industrial Engineering in Sweden and the only course of all these courses I have not needed to take is the boolean algebra. Thank you for the video!
Slide 3:19 is VERY wrong. This notation basically multiplies the matrix by the vector, which is not the same as written above.
Correct, he forget (x
y
z) part
*I mean the notation with these variables*
This is the best description I have seen. @Tamer Shaheen Keep up the good work.
Thanks for the video man! It’s very helpful. I’m studying mechanical engineering (fluid mechanics, heat transfer…) and I’m really struggling with Matlab right now. Do you know any good books (with examples and problems) that can help me, please? I’ll be very thankful and good luck 😉
I’m sorry but idk of any good MATLAB books 😅 I just learned it all through RUclips videos
@@TamerShaheen could you recommend to me some courses or channels on RUclips. Appreciate it bro!
Thank you alot . You tell us what didn't lectureres at university didn't tell us♥️♥️
in india we have jee exams, never knew calculus had 3 parts 😐
Worked as an electronics engineer for 40 years. Did a lot of motion control. Used laplace transforms and complex algebra constantly throughout my career. Designed circuits and wrote code that performed derivatives, integrals, and filters. Only once did I actually calculate an integral equation, but I had to correlate a theory with data we took.
I’ve used math from every single math class I took in my mechanical engineering degree. It all has really world applications. Don’t fool yourself thinking it has no applications
True. Most engineering students cannot even see how something they learned in the first semester is connected to and used for some more advanced class. So that's why few people can actually figure out how to use math in real life.
I'm a software engineer and I only ever had to go through Calculus II, Calculus III and Linear Algebra were optional as elective courses but there were other
"After you graduate from engineering, you do very little math." I don't remember a single day where I didn't use calculus, complex frequency analysis, or algorithms for EE system design and embedded firmware in wireless SoC 😂
I swear you guys don't get paid enough
You may use it, but don't do the problems by hand, which I think is the point of the video. Imagine doing bode plots by hand. haha
Thanks for your sharing!! it helps me a lot
Financial Management is probably the only useful course after graduation....
absolutely
I’ll have to say that philosophy is also needed
Engineers right out of school typically solve very little math with paper and pencil, but if you climb the ladder, there is a much higher chance of using more advanced mathematics. And it depends wildly on role and field.
*Cries in Abstract Algebra* Not an engineer, but yeah. That can be difficult.
Tamer Shaheen nice video!