I'm 75 and had advanced math courses. I have been doing his popup quizzes for 2 months as an attempt to remain nimble of mind. He has math courses for all MATH. Why is MATH important? 1. CALCULATORS become a crutch but not always the answer. 2. Many schools offer "more interesting" courses in place of MATH. 3. We need to exercise are body and our MIND! 4. You gain self-esteem by being proficient in MATH. 5. Success in MATH yields success in LIFE. Keep up the good work.
May I suggest that you make a correction to this video? You wrote dx/dy, instead of the proper dy/dx. I noticed it immediately but uncritically because that kind of mistake can happen to any of us in the flow of discussion. I kept expecting you to notice it yourself and correct it, but you didn't. As the discussion progressed, you erased it, then, to my amazement, you wrote it again and verbalized it. The repetition may really cement it into the minds of true beginners. I suppose the effect on them is likely to be trivial; they'll no doubt get it sorted out quickly enough if they continue to pursue the study of calculus.
In high school and college I was always intimidated by higher math, not because I didn't understand it but rather because I have severe test anxiety. It sucks. But I'm now 51 years old and have been a software engineer since 24. Math has been integral in my career. These videos make revisiting math fun and enjoyable. 🙂👍 I'm so glad my kids do not share my anxieties. Thank God.
I was so scared of math when I was young I didn't dare take higher math. So at 70, I realized that those fears were because I had a weak concept of Algebra 2. It still makes my head spin, but I appreciate computers and videos that I can pause and proceed at my own speed.
@@markellinghaus8901 LOL .. I started to study it "JB" and now is helping me at work being better at troubleshooting problems and organizing better the aproach to fix them. Good to hear about this community.
I’m still trying to re-learn algebra, it’s been 23 years since I took a class. This lesson blew me out of the water, so I really need to learn algebra better to ‘get’ this. I’m really enjoying this lesson and I’m looking forward to learning more.
This is the way calculus should be presented--pique interest and understanding first, before getting into the application. I dropped my first calculus class in college because the prof started into a problem with a "well, let's see" approach when I didn't even know what he was doing.
I can appreciate this instructor's enthusiasm. That's one sign of a good teacher. But I believe that he misspoke toward the end of this video when says that the top of the parabola is (4,-7), when it is actually the other way around, (-4,7).
@@JakeRichardsong On watching the video again beginning at roughly 16:46 you’ll see that he quickly erases the -7 and rewrites a dashed line that represents the line y = 7, and not -7. And he also has his coordinates written as (-4, 7), which is correct, -4 = x, and 7 = y.
I never thought I would need any of this while in school, though in the recent years I have had to tackle many task which needs not only calculus though lots of other styles of math also. Almost everything in the 3D designing and game developing requires such knowledge, and same with sound engineering, though the cool thing about sound engineering mostly everything on the energy frequency spectrum is universal, so if your knowledgeable with radio waves then you will do well with microwaves.
Surprisingly game development is actually becoming far more straightforward. Writing engines and then shaders that take three dimensional calculations and then reverting them to two dimensional rendering was really difficult, woo matrices... don't get me wrong, all the power behind the new free to use stuff that does 99% of the backend stuff for you is awesome, but it's the sheer computational ability of modern gpus and cpus to forego alot of the necessity to save every bit(no pun intended) you could and take every shortcut you could that allows things to truly shine now. I laugh at some old engines I've written that can run at 200,000 fps uncapped now when they used to run at 80 nicely lol. Also have a big pile of burnt out components... don't write bad code kids.
"never thought I would need any of this while in school". This is the misinterpretation often heard. It is what you learn, it is the learning process you are learning at school. And off course this comes in handy if you want to be a doctor or a chemist or a financial expert, etc. It is all about learning, not if you need this in future.
It’s not even dy/dx - in this case it should be df(x)/dx. dx/dy is obviously meaningless in this case, as that would be the rate of change in x due to a change in y - yet there is no y in this equation!
Dude, two issues: 1. It's dy/dx, meaning the rate at which the values of y are changing with respect to x. To be sure, there's also dx/dy but it's a different issue all together. 2. By now, you should've noticed the problem and perhaps make another video.
It would be helpful to demonstrate exactly what problem this exercise actually solves. As I understand things, if a cannonball shoots up in this kind of parabolic arc, then after the halfway point (where the slope is zero), it takes the same amount of time to descend as it took to ascend up to that halfway point. You could inject something like that into the video -- or perhaps predict how far away the cannonball will land. It's still only a vaguely practical aspect, but it would get students thinking about the applied usefulness of these problems.
I agree. Calculus teaching often seems to miss the "but why would I want to do this" aspect. For instance, at 4:55 this video says Integration is the way we can find area under a curve. But WHY would we want to find the area under a curve? What's the practicality of this for a school student? Sadly this isn't explained to the beginner here.
I absolutely agree, as a current highschool student in Ap classes not a single teacher actually explained what these are used for. So I'm having to relearn the subject basically so that I understand what's happening. I can solve numbers not irl things.
If you change the word "slope" for "rate of change", then you start to get into real world applications. For example. the rate of change of distance with respect to time is velocity. And the rate of change of velocity with respect to time is acceleration.
Well had a minor in mathematics up through differential calculus that is when it all made sense to me, but it was a struggle up to that point. If I had this understanding earlier would not have spent hours of homework trying to understanding the basics when I first started. Thou rusty now this was nice reminder. :) Well done!
Derivative is rate of change. Rate of change is just another way of talking about a slope and to find the secant (average slope) of a function you take y2-y1/x2-x1. So, the slope ends up being some kind of y/x. Taking the derivative of a function finds the rate of change as well (like a slope) so Derivative is dy/dx.
I enjoyed this video. I was a math minor in college many years ago and have forgotten much about calculus. After being a pilot for my career, yes, there wouldn't be aviation without calculus. I think I'll go find my calculus book and play around with it. It's better than solitaire.
Thanks for the lesson. You mentioned the big picture in the beginning and I think that is so important for the student to comprehend what they are doing. We had a professor in engineering school who always advised when taking derivatives what exactly we are looking at and that is the rate of change if one variable with respect to another. He mentioned this over and over again to beat it through our heads what exactly we are looking at
Probably will be my last Calculus problem!!!!!! LOL!!! Thanks for the video, took Calculus many years ago and didn't do too bad at the time and was applied to our Electronics designs. It is kind of math if you don't use it, you loose it. Just like Algebra and Geometry - all the rules. Thanks for the video, take care
I am 68 y.o. with degree in mechanical engineering which means 4 semesters of Calculus in college I took almost 50 years ago. I stumbled upon this video and what I did when the problem was posited, I froze the video to see if I could solve this elementary calculus problem. I did and got the right answer...first derivative and setting the first derivative = 0 and solving for x. Calculus throughout my life has been something I thought about but rarely used. The gift of learning is the greatest gift of all and I am forever in debt to my brilliant college professors and colleagues I worked with throughout my career. My major in college used the highest level of math which was partial differential equations and even when very young it was most challenging. Thanks for channel. You are a great teacher.
When I was learning calculus in high school, the teacher demonstrated the power rule. It was simple, but it confused me because I am the type of person that likes to understand things. I went home that evening, and found the derivative by definition, AFTER which I started applying the power rule. I do not understand why I would tell people I know some calculus if I do not understand why it works!
This is the kind of stuff that would confuse me: where did the quadratic equation come from? Where did f(x)= -xsquared- 8x - 9 come from? Do They just magically appear on every calculus problem? I feel cheated that math is taught almost backwards. I need to see the big picture. Why couldn’t some teacher take a class during algebra 2 and do a calculus problem showing how the quadratic equation is used? It would have made learning it a lot easier.
no, when it gets difficult you have to work out the function yourself, for a first go you don't need the extra complicaton, just go with it for now. If you want to learn to juggle while riding a bike, first learn how to ride the bike, then learn how to juggle, then try to do both together.
It’s the equation that enables you to draw the graph. An x^2 graph is a parabola. To draw the graph input values of x from say -8 -6 -4 -2 0 2 4 6 and 8 into the -x^2 -8x -9 equation to get y values. The rest essentially moves the parabola around the x y axis on the graph paper. The minus x^2 at the start moves the parabola to the left of the y axis on x=0. The minus 8x and -9 also changes where the parabola is drawn. I would recommend trying drawing graphs but changing the value -1x^2-8x-9, x^2-8x-9, x^2- 8x+9, x^2 -8x + 0 Hope that helps
Agreed. He just wrote it but did not say what it was. And even wrote it upside down! Should be dy/dx ie the change in y resulting from a small (actually infinitesimal) change in x, as a fraction. Also called rise over run, or slope.
In Dutch we call it differentiation and integration. I remember having learned integration before going to university ( but not in order to study mathematics : ) )
i’ve always been interested in advanced math like this but haven’t been able to learn in school. this is because of my own mental health issues aiding in depleting my grades, so i’m unable to learn anything new and am forced to redo simple classes until graduation. i likely won’t be able to attend any college after i graduate. the education system doesn’t seem to actually look out for students from a humanistic standpoint but rather as a way to get kids in and out so that they’ll be able to function as slaves to our economic system.
what an appallingly bad teacher!! He wastes so much time repeating himself with endless waffle and not actually explaining anything, for example what IS a derivative?!
I never learned calculas. I understood the graph, slope, highest point and negative motion of slope. But I could not understand what is d what is f and where from 8 and 9 came practically.
Good explanations. The movie Stand and Deliver is "the story of Jaime Escalante, a high school teacher who successfully inspired his dropout-prone students to learn calculus." I've always been curious if he just taught to a level his students could understand, like your doing here, had tricks or short cuts or just took the time needed to ensure each student understood the material. Any thoughts?
Sorry to go off topic, but my wife and I watched that movie on our Honeymoon in 1989, we were at a cabin in the mountains for a week and I rented us a bunch of movies. I still remember Stand & Deliver, and Gorillas in the Mist after 4 kids and 33 years.
From basic math conventions, y is always the dependent variable, and equals f(x), and x is the independent variable. This convention is observed to this day in most areas of math ranging from algebra, calculus, statistics, all the way through machine learning to deep learning. Accordingly, a better notation would be y = f(x), dy/dx rather than dx/dy. Especially these days with widespread use of AI/DL/ML, it would be good to train young minds right from the start to use the correct conventions. Also, while this is great, it seems like it could be much more concise. just my .000002
I doubt the teacher John knows that the entire engineering is based on dy/dx (gives deflection) and second derivative is d^2y/dx^2 (bending moment) etc.
Schools want us to learn this but not credit score, credit card debt, household financial management, college loan debt. No wonder everyone is in debt up to their eyeballs.
Hi!! Thank you so much for this video. I have to take a calculus class for my BA major. I haven’t taken a math class in 5 years. I was scared but watching this video made me realize that it’s not so scary and I can do this! ❤
Even though I have published and taught applied quantitative analysis for many years, my knowledge of calculus has been the slope of a horizontal line mentioned in your video. I now know how to create a derivative and find the high point of the parabola. I like your passion for the material and sincerity. However, I suggest you eliminate the irrelevant commentary found throughout the lesson. It is distracting and detracts from your otherwise fine explanation. Thanks for making these videos.
I’m in the 5th grade (like you probably depending on where you live) I’m also eleven. I want to be a mathematician and I’m trying to get ahead. So I’m watching math videos all day
Dy /dx is the derivative of y with respect to x, while dx/ dy is the derivative of x with respect to y. However yoir example shown f'(x ) so it shud be dy/dx
In 1966 I was flunking math in the Knavey’s nuclear power school. When I asked for help the instructor told me, “Read the book!” The text book was terrible, it caused me more confusion than anything else. I flunked out out of nuke school. Which, as I learned later, you really had to be really, really weird to enjoy duty on submarines! I could have used a good instructor like yourself, however, I may have become really, really weird.
Could you just do it and quit talking, I'm not interested in your history, just the topic of your video!!! 3 minutes and you're still not into the topic, it's like watching grass grow, or paint dry...
13:01. Now I am thoroughly confused. When you’ve got one to the second power, shouldn’t you be multiplying 1×1, which would equal one? You don’t multiply the power by the number? You multiply the number by itself, as many times as the power tells you to? Is this something different?
I completely understand your confusion, John. The rule in finding the derivative is that you multiply the exponent by the coefficient to find the new coefficient. Afterwards, you decrease the original exponent by one to find the new exponent. Here are some examples: 2x^3 becomes 6x^2, 3x^2 becomes 6x, 4x^5 becomes 20x^4, -4x^4 becomes -16x^3, 5x becomes 5, and 3x^-2 becomes -6x^-3. Hope this helps.
@kdjayo1 : He is using a standard formula. If y=x^n then dy/dx= nx^(n-1) This formula can be derived by methods that are known as ‘first principles’ and requires knowledge of the Binomial Theorem and a concept called ‘limits’. So frankly this is not the way to teach the ‘first calculus problem’ as he puts it. This is actually a problem on maxima and minima and comes much later in calculus, there are numerous other things you need to know before you get here. If you really want to understand Calculus, you must learn the first principles. Your fundamentals will be strong then and you can then master this subject.
@ Tyler Michael Hoffman What do you do when you run across a function like this, f(x) = 8x^8 + 12x^5 - 4x^4 + 10x^3 - 6x + 5? Calculus works every time for both types of functions. -b/2a only works for quadratic equations. This is calculus class. He doesn’t want to use -b/2a. He only wants to teach viewers how to find where a curve’s slope is 0 using only calculus. Now… if this were an algebra class…
Does every calculus problem start with 3 minutes of dribble? Get to the point then the upsell, check out the RUclips marketing videos. Offer something before you beg for something.
Blame RUclips. RUclips currently ranks videos based on length so creators have compensated by lengthening their videos to receive a higher ranking. But he could have added more substance instead of babbling on.
This video seems to me is very useful. But, according to this equation, I would like to know about -9 . I didn’t see you mentioning? Thank you for teaching me. Michael Mai
It was the rules in getting the derivatives of a function, -9 is a constant number and according to the rules on getting the derivatives all the constant numbers is equals to zero. Hope you understand it.
FWLIW: The frustration I've always had with 'higher' maths as someone who has no real interest or need but would at least like to understand: -Here are the concepts - ok, no problem. Please don't muddy things by restating half a dozen different ways, do it right just once. -Here's a bunch of different ways to write those concepts - ok, but just those required for now would be less confusing. -Now we'll do a bunch of unexplained manipulations, and there's the result - that might as well have been magic! It's been my experience that most maths teachers will happily define the concepts multiple ways on the misapprehension that is where their students are confused and more explanation must surely be better rather than more confusing. They then demonstrate all the ways in which the problem may be stated under the equal misapprehension that their students are as fascinated as themselves - nobody is fascinated by having the expectation that they are about to be made to feel stupid rubbed in their face. The 'teacher' will then inevitably go on to show the process like a conjurer performing a trick as if said process itself is the most obvious thing in the world, culminating in a result that will seem to be impenetrable magic to most of their students. The process is never explained, just presented. It is these ill explained nuts and bolts that link the start and finish where all the confusion is to be found. Very frustrating! Some advice for budding teachers, especially maths teachers who tend to be those who most desperately need such advice: -Define the concept(s) required as clearly and succinctly as possible, ONCE, and in only ONE way. Check CAREFULLY that EVERY student gets it and if not CAREFULLY enquire what it is they are struggling with and address those specific issues ONLY. -Once EVERYBODY is on board introduce any new tools required and ONLY those tools. If it's a maths concept or problem DO NOT introduce multiple notations or methods, stick with ONE and choose the most conceptually straightforward if there is one. -Make absolutely sure EVERYBODY understands the purpose those new tools, especially their meaning, before ANY further steps are taken. -Only now is the time to work through illustrations and examples. The following is where 90% of maths teachers loose 90% of their students. -DO NOT under ANY circumstances run through your examples as if they will be as obvious to your students as they are to you. Many will be instantly turned off as they see the widening gap between their lack of understanding and the impression their poor teacher is giving that it should be easy. Of those few still following along most will have an unnecessarily frustrating devil of a time keeping up. The very few who have no issues will fool you in to thinking all is well - they won't understand what is wrong, destined as they are to regrettably become the next generation of 'teachers'. -INSTEAD go through EVERY step and symbol in excruciating detail, being very sure that every assumption, implication, and procedure, is unpacked for the clear understanding of all. It is at THIS POINT that NEARLY EVERY maths TEACHER FAILS NEARLY EVERY STUDENT - take your time and do it properly! -The bells and whistles may be imparted later to those who care and have the ability to grasp them.
this and this and this again . I have no problem with the notation, explained over and over again. I can remember how to magically manipulate the equation. I have no idea of what I am doing because the fundamental concepts underlying the operation are missing.
F(x) is y. With functions, the y-coordinate is a “function” of x, meaning whatever x-value goes into the equation, the equation around it gives the value of y. For example, if the function was f(x)=x+2 then y would equal any x value +2. If x were 3, y would equal 5. And if x were 10 y would equal 12. This is how we conceptualize a changing line, with y being a function of x, or f(x).
You could make math obtainable to anyone interested. If you developed a program that tutored a student while doing problems. The key would be to have the program recognize a mistake and tell the student. But most importantly tell the student what the mistake is and what concept he is missing. I’m a retired lawyer when I went to law school we had very basic computer computers. But we had one program for evidence. In it you would have an issue which you’d rule on if you were wrong it would tell you why. It was basic but powerful. You could really get the hang of it. I think a math teacher and a computer programmer could revolutionize teaching of math. At first I thought it would be good for calculus and it would but it would be great for any level math. Also video type games could be developed to give practical application too. I wish I knew a math teacher and a programmer who wanted to bring calculus to the world. Calculus is the big separator of intelligent people. Many intelligent people can’t get it. It’s a shame but a constant tutor available would make it doable for any above average intelligent person! 17:42
I had to take business calculus at the beginning of Covid and let me tell you no one knew how to deal with this. We spent two weeks not doing anything and then finally I think the school said just try and get them to pass a class anyway possible and my professor said since we are doing everything online now you get to use your notes you get to help each other and you get to pair up with people taking the final and I passed the class with a B. That was pretty rough.
Set the equation to 0 and solve for x. For exanple if the equation is y=-x^2+12x-27, then we can see where it crosses the x axis if we set it to 0. So 0=-x^2+12x-27. Now solving for 0 we get x=3, and x=9. That means at x=3, it's on the x axis (floor) going up. And at x=9, it came back down to the ground
Careful! A number of slips of the tongue in this one. Would derivation of the 'rule' be helpful here rather than just saying, "This is the Rule"? Is there a table of rules available for Calculus , like in Geometry ?
Your video is mostly on point except when you say dx/dy, that is NOT the same as dy/dx when taking the derivative in the first way you stated you are taking a function that depends on x but taking its derivative with respect to Y which requires either finding its inverse as a function of Y or implicit differentiation.
@P0LAR0 He took the derivative of the function f(x) = -x^2 - 8x - 9 which gives the function f’(x) = -2x - 8, which is the derivative function. The derivative of -9 equals 0, so there’s no need or point in writing the 0. You simply write f’(x) = -2x - 8. He got -4 by setting the derivative f’(x) = -2x - 8 equal to 0, like so, -2x -8 = 0, then he solved for x, which gives -4. Don’t know what you mean when you ask “how did the - turn to +.” Or I should say that I don’t see where that happens here. What do you mean in asking that? And what do you mean in asking “how he got the 9? First, there’s no 9, there’s a -9. And that -9 is simply one of the terms in the equation f(x) = -x^2 - 8x - 9, is all.
Thank you so much!... the way you explain is beyond good, you have a talent for this!... I am taking advanced macroeconomics now, and I started watching this for fun, and I stayed because you are actually putting a picture on my head!
I took calc all the way through differential equations when I was in college. According to K-12 standardized test scores I had great aptitude, but I except for 8th grade algebra when I had a gifted, fabulous teacher I always avoided math because I never really could make it fit together. I thought I was just stupid. Then in my first college math course I got very lucky again and found a teacher that changed my learning life. I had him for college math and algebra but then had to take my first calculus class without him. I dropped it. It was then that I realized a lot of my issues really did have to do with the teachers and the way they taught, and I wasn’t just stupid. But I had finally discovered that I really did love math, so I tried again. After I transferred to a different college I got another fabulous teacher and stuck with her from Calc 1 through “diffy q’s”. I had to work really hard... I took detailed, voluminous notes, and did all my homework three times, Lol...but I got straight A’s. I also became a successful tutor for a while. Many of my students told me I broke it down better than their teachers and their test scores improved dramatically. I considered going into teaching but decided against it, largely because of the curriculum for educating teachers. Comprehending math changed my life. It structured my thinking and even helped my writing ability. I was able to write things more clearly because math and specifically calculus had taught me how to pick a problem apart and put it back together to arrive at an orderly, effective solution. Calculus is bar none one of the great brain growing tools of all time. It’s been 20 years since I finished my DE class. This popped up on my RUclips feed so I decided to give it a watch for a quick, fun refresher. And I gotta say, while I admire the spirit in which this guy is trying to help, if I was a neophyte, struggling student with no previous knowledge of calculus, this wouldn’t have made much sense to me at all. I would have zeroed right out of his Calc class in short order. He’s all over the map. It’s obvious that math and Calc is something that just always kind of made sense to him, and he doesn’t break it down in a way that’s conducive to the kind of structured, almost rote approach that many of us knuckle draggers need to really comprehend and internalize math. The majority of students are knuckle draggers when it comes to math. I can say that because I was one. One of the things I realized during my math journey in college is that I did not need to grasp the concept being taught immediately in order to be successful. Concepts are important, but it’s not always imperative that they be completely understood immediately in order to achieve success in the classroom. My Calc teacher would sometimes tell us that she was going to teach us the mechanics first and circle back around to the concepts, and also why she was doing it that way for this particular section. It worked! I learned that if I was given a formula and I could memorize it well enough to break a problem down well enough get the right answer for a test, the concept ALWAYS came to me eventually. Sometimes it was sooner, and sometimes it was later. A couple of times the aha moment actually happened during the test while I was working a problem. Lol. The point is that if I could memorize and learn the mechanics well enough to achieve outstanding success on the test, I ALWAYS internalized the concept behind the mechanics at some point. This guy doesn’t spend enough time on the mechanics, IMO. Rote learning has fallen out of favor, but there’s a huge gap in our education process and our education outcomes because of it. The insistence on complete conceptualization at the expense of the hard work of rote learning is where education in general but math education in particular has been failing our young people for over 40 years. Rote learning is a necessary prerequisite to success for all but a fortunate few. And most of us are never going to go on to be engineers or physicists, so we will never use algebra, trig, or calculus for anything practical in our lives. So if the arcane concepts of slope and area under a curve fade for us over time...that is to say, if the larger concepts fade...its not really any harm. But the restructuring of our brains incurred by learning how to pick a problem apart at the mechanical level and arrive at a correct solution, will never leave us. That kind of learning is crucial in life. It’s not popular in modern teaching theory and it’s not popular with students cuz the mechanics are hard work, but teachers especially math teachers who don’t ultimately grasp this concept are doing their students a grave disservice. Just sayin’ in case that helps. This vid gets an A for effort and heart, because it’s in the right place. I think this guy loves his students and he loves math. But it gets just a C for overall effectiveness, which is what really counts.
I think this is an interesting review. It also points to a lot of issues with math teachers. Like you, I have had the good, bad, and ugly when it comes to having a good teacher, especially math. To this point (for the sake of intelligent conversation), I find myself agreeing with you and simultaneously disagreeing with you (pertaining to me, specifically). In some facets, math was easy. In others, insanely difficult. And not because the math was difficult, but it was too rote; too meaningless; too arbitrary. For me, I needed to understand the concept before the mechanics. I needed to have a reason. There had to be a story. While I agree that a story cannot exist without letters (surely one can not write a story without knowing their letters), it provided a direction for my thinking. Otherwise, there was no use in understanding the letters because the story didn't have meaning anyway; interest was lost. It seems people that teach math are those that tend to be good at math. In other words, it came natural to them. For those types of people, it is difficult to understand how us knuckledraggers (love that word) are not getting the concepts. Consequently, they teach as they "see" things. And it's really like this in all academia but math is entirely a different language. It demands structure (which as you indicated, one of the very beneficial things about learning math). For example, I teach psychology. My first class gave me terrible reviews, lol. I had no clue why. As it turns out, I talked over everyone's head but did not have a clue until later talking to the students. Why? It is my passion; something that I understand and place together very easily. It was difficult for me (even having experienced this same issue from math teachers) to see that I was doing the same thing to those poor souls. In fact, psychology is one of the reasons I came to appreciate math (as odd as that may seem). I could see the patterns but was lost in the mechanics/language. Which is why I agree with you about the mechanics being important, but most people do not have the same success from rote memorization (statistically speaking). This is why understanding from your insane work ethic (which is awesome, btw) improved your ability so much; it clicked and you got it! Sadly, I was never taught either sufficiently. I learned more from youtube videos than I ever have from any classroom, though I have had some good teachers years ago. And, it wasn't required for me to learn deep maths, but I have always been the guy who learns things differently, often in reverse of everyone else. Anyway, I found your comment intriguing. Made me evaluate things....which is the predicate of mathematics, ironically. So thank you.
17:50 he misspoke by saying "negative 7 4" when its "negative 4 7." It was written correctly though, I'm an old fart and still like math. good easy basic, first problem and explanation of such.
At 1:59...2:01 "My program is very unique". There is no such a thing as very unique. Unique is unique. Neither less, nor more . Nor little, nor some, nor very. Just unique. OK, so the English language is not you subject. But repeatedly you've made the biggest howler I've ever seen a maths (yes, mine is British English) teacher guilty of. "(dx)/(dy)"....that is utter nonsense, unless the y-axis is horizontal and the x-axis vertical. Need I say more?
I am a 79 year-old Ivy League Spanish major - (Cornell '67) - never took calculus, and found this video perfectly understandable. The derivative and the calculation of derivative finally make perfect sense to me. I now feel ready to learn more math from TabletClass!
I'm 75 and had advanced math courses.
I have been doing his popup quizzes for 2 months as an attempt to remain nimble of mind.
He has math courses for all MATH. Why is MATH important?
1. CALCULATORS become a crutch but not always the answer.
2. Many schools offer "more interesting" courses in place of MATH.
3. We need to exercise are body and our MIND!
4. You gain self-esteem by being proficient in MATH.
5. Success in MATH yields success in LIFE.
Keep up the good work.
My high school maths teacher didn’t explain calculus this easily and nicely. Excellent lesson. If you know algebra this stuff is a picnic.
I wish all instructors were as clear and provided simple instructions. Great work!
May I suggest that you make a correction to this video? You wrote dx/dy, instead of the proper dy/dx. I noticed it immediately but uncritically because that kind of mistake can happen to any of us in the flow of discussion. I kept expecting you to notice it yourself and correct it, but you didn't. As the discussion progressed, you erased it, then, to my amazement, you wrote it again and verbalized it. The repetition may really cement it into the minds of true beginners. I suppose the effect on them is likely to be trivial; they'll no doubt get it sorted out quickly enough if they continue to pursue the study of calculus.
In high school and college I was always intimidated by higher math, not because I didn't understand it but rather because I have severe test anxiety. It sucks. But I'm now 51 years old and have been a software engineer since 24. Math has been integral in my career. These videos make revisiting math fun and enjoyable. 🙂👍 I'm so glad my kids do not share my anxieties. Thank God.
(X-9) ( x+1)
What kind of software engineering do you do? I graduated with degrees in computer science and applied mathematics and I rarely used math in my career.
@@bjbell52 I was asking myself the same thing
@@bjbell52 he’s a liar
He is a liar because you are believing a false prophet. All men are liars.
Not sure how I ended up watching this video, but I watched it all the way through. Wish I had a teacher like this for when I struggled with math.
I know why I'm here because I suck at math and I'm trying to listen . Lol 😆
This guy has such a one on one voice I also wish I had a teacher like him
Same.
@Ralph Reilly yeah haha I would humbly suggest this is not a very clear explanation. Much better way to explain.
@@cattnipp So where do I find your videos on the subject?
I was so scared of math when I was young I didn't dare take higher math. So at 70, I realized that those fears were because I had a weak concept of Algebra 2. It still makes my head spin, but I appreciate computers and videos that I can pause and proceed at my own speed.
Are you reviewing math at 70 ? If so.. it's great to know I am not along. LOL
Makes a few of us boomers reviewing this topic.
I'm 72 and decided to learn graph theory, for which I have to learn matrix analysis, for which I have to learn Algebra II and Calc. 😀
@@markellinghaus8901 LOL .. I started to study it "JB" and now is helping me at work being better at troubleshooting problems and organizing better the aproach to fix them. Good to hear about this community.
great to hear - you are not alone, math gets the wheels turning even at 60+ yrs
While other calculus videos aim to discourage us to take calculus, you encourage us.
I’m still trying to re-learn algebra, it’s been 23 years since I took a class. This lesson blew me out of the water, so I really need to learn algebra better to ‘get’ this. I’m really enjoying this lesson and I’m looking forward to learning more.
This is the way calculus should be presented--pique interest and understanding first, before getting into the application. I dropped my first calculus class in college because the prof started into a problem with a "well, let's see" approach when I didn't even know what he was doing.
Using dx/dy is incorrect, it should be dy/dx
Yes huge mistake and very sloppy, it is hard to think that any maths teacher would make this error.
Yeah Change in Y / Change in X
@@zomisintu Correct. He has his change in Y confused with his change in X. He has to swap (invert) both to get "dY / dX."
However, dx / dy = 1 / ( dy / dx ) legitimately.
I can appreciate this instructor's enthusiasm. That's one sign of a good teacher. But I believe that he misspoke toward the end of this video when says that the top of the parabola is (4,-7), when it is actually the other way around, (-4,7).
Yes, the 7 is not negative, that error confused me at first.
@@JakeRichardsong
On watching the video again beginning at roughly 16:46 you’ll see that he quickly erases the -7 and rewrites a dashed line that represents the line y = 7, and not -7. And he also has his coordinates written as (-4, 7), which is correct, -4 = x, and 7 = y.
I'm very interested in learning more, you made it easy to understand wish you could teach my class. Thank you!
I never thought I would need any of this while in school, though in the recent years I have had to tackle many task which needs not only calculus though lots of other styles of math also. Almost everything in the 3D designing and game developing requires such knowledge, and same with sound engineering, though the cool thing about sound engineering mostly everything on the energy frequency spectrum is universal, so if your knowledgeable with radio waves then you will do well with microwaves.
Surprisingly game development is actually becoming far more straightforward. Writing engines and then shaders that take three dimensional calculations and then reverting them to two dimensional rendering was really difficult, woo matrices... don't get me wrong, all the power behind the new free to use stuff that does 99% of the backend stuff for you is awesome, but it's the sheer computational ability of modern gpus and cpus to forego alot of the necessity to save every bit(no pun intended) you could and take every shortcut you could that allows things to truly shine now. I laugh at some old engines I've written that can run at 200,000 fps uncapped now when they used to run at 80 nicely lol. Also have a big pile of burnt out components... don't write bad code kids.
"never thought I would need any of this while in school". This is the misinterpretation often heard.
It is what you learn, it is the learning process you are learning at school. And off course this comes in handy if you want to be a doctor or a chemist or a financial expert, etc.
It is all about learning, not if you need this in future.
I Failed Calculus in 2010, your video came out 1 year ago, this would have helped so much
Awesome man. I wish we had all these RUclips videos around when I went to college. Nevertheless you are a great teacher…👍👏👏👏🙏
Graph the line -2x-8 and show that the vertex of -x^2-8x-9 occurs at the x-intercept of the the line.
In this video, you were saying “dx/dy.” Actually, it is “dy/dx.”
Exactly
@@acbulgin2 , yes I have noticed that. At first I thought it was just a human mistake...then I realized it is really lack of knowledge....so, I left
It’s not even dy/dx - in this case it should be df(x)/dx. dx/dy is obviously meaningless in this case, as that would be the rate of change in x due to a change in y - yet there is no y in this equation!
@@stevenproud6167 , that is even more correct
Dude, two issues:
1. It's dy/dx, meaning the rate at which the values of y are changing with respect to x. To be sure, there's also dx/dy but it's a different issue all together.
2. By now, you should've noticed the problem and perhaps make another video.
It would be helpful to demonstrate exactly what problem this exercise actually solves. As I understand things, if a cannonball shoots up in this kind of parabolic arc, then after the halfway point (where the slope is zero), it takes the same amount of time to descend as it took to ascend up to that halfway point. You could inject something like that into the video -- or perhaps predict how far away the cannonball will land. It's still only a vaguely practical aspect, but it would get students thinking about the applied usefulness of these problems.
I agree. Calculus teaching often seems to miss the "but why would I want to do this" aspect. For instance, at 4:55 this video says Integration is the way we can find area under a curve.
But WHY would we want to find the area under a curve? What's the practicality of this for a school student? Sadly this isn't explained to the beginner here.
I absolutely agree, as a current highschool student in Ap classes not a single teacher actually explained what these are used for. So I'm having to relearn the subject basically so that I understand what's happening. I can solve numbers not irl things.
If you change the word "slope" for "rate of change", then you start to get into real world applications.
For example. the rate of change of distance with respect to time is velocity. And the rate of change of velocity with respect to time is acceleration.
Well had a minor in mathematics up through differential calculus that is when it all made sense to me, but it was a struggle up to that point. If I had this understanding earlier would not have spent hours of homework trying to understanding the basics when I first started. Thou rusty now this was nice reminder. :) Well done!
Very well done!
Derivative is rate of change. Rate of change is just another way of talking about a slope and to find the secant (average slope) of a function you take y2-y1/x2-x1. So, the slope ends up being some kind of y/x. Taking the derivative of a function finds the rate of change as well (like a slope) so Derivative is dy/dx.
I enjoyed this video. I was a math minor in college many years ago and have forgotten much about calculus. After being a pilot for my career, yes, there wouldn't be aviation without calculus. I think I'll go find my calculus book and play around with it. It's better than solitaire.
Thanks for the lesson. You mentioned the big picture in the beginning and I think that is so important for the student to comprehend what they are doing. We had a professor in engineering school who always advised when taking derivatives what exactly we are looking at and that is the rate of change if one variable with respect to another. He mentioned this over and over again to beat it through our heads what exactly we are looking at
I agree, I’m learning all these calculations, solving problems, but don’t know how to apply the information into making real-world designs
You😅
Great example!!!
Probably will be my last Calculus problem!!!!!! LOL!!!
Thanks for the video, took Calculus many years ago and didn't do too bad at the time and was applied to our Electronics designs. It is kind of math if you don't use it, you loose it. Just like Algebra and Geometry - all the rules.
Thanks for the video, take care
Leibniz' commonly used notation for the derivative would be dy/dx, not dx/dy as described here....
I am 68 y.o. with degree in mechanical engineering which means 4 semesters of Calculus in college I took almost 50 years ago. I stumbled upon this video and what I did when the problem was posited, I froze the video to see if I could solve this elementary calculus problem. I did and got the right answer...first derivative and setting the first derivative = 0 and solving for x.
Calculus throughout my life has been something I thought about but rarely used. The gift of learning is the greatest gift of all and I am forever in debt to my brilliant college professors and colleagues I worked with throughout my career. My major in college used the highest level of math which was partial differential equations and even when very young it was most challenging.
Thanks for channel. You are a great teacher.
You are my fathers age. He will turn 71 years old this year. He is a retired electrical engineer 👷♀️
right Diffy Eqs! killer!
you are not a lone geezer❤
Joe helped me a lot with algebra 2 and I got fairly good with it.
Warching
A highly motivational lesson to learn mathematics. Thank a lot
I always got confused with the different notations nevermind the number crunching. Good lesson.
When I was learning calculus in high school, the teacher demonstrated the power rule. It was simple, but it confused me because I am the type of person that likes to understand things. I went home that evening, and found the derivative by definition, AFTER which I started applying the power rule. I do not understand why I would tell people I know some calculus if I do not understand why it works!
Young man, in mathematics you don't understand things. You just get used to them. - John von Neumann
Just curious (-4,-7) therefore, it is in quadrant 3. This is inverted parabola.
This is the kind of stuff that would confuse me: where did the quadratic equation come from? Where did f(x)= -xsquared- 8x - 9 come from? Do They just magically appear on every calculus problem?
I feel cheated that math is taught almost backwards. I need to see the big picture. Why couldn’t some teacher take a class during algebra 2 and do a calculus problem showing how the quadratic equation is used? It would have made learning it a lot easier.
no, when it gets difficult you have to work out the function yourself, for a first go you don't need the extra complicaton, just go with it for now. If you want to learn to juggle while riding a bike, first learn how to ride the bike, then learn how to juggle, then try to do both together.
It’s the equation that enables you to draw the graph.
An x^2 graph is a parabola.
To draw the graph input values of x from say -8 -6 -4 -2 0 2 4 6 and 8 into the -x^2 -8x -9 equation to get y values.
The rest essentially moves the parabola around the x y axis on the graph paper.
The minus x^2 at the start moves the parabola to the left of the y axis on x=0. The minus 8x and -9 also changes where the parabola is drawn.
I would recommend trying drawing graphs but changing the value -1x^2-8x-9, x^2-8x-9, x^2- 8x+9, x^2 -8x + 0
Hope that helps
Thank you for demystifying calculus!
We need you to explain precisely what the d means in the expression dy/dx. Presumably, it means change (delta).
Agreed. He just wrote it but did not say what it was. And even wrote it upside down! Should be dy/dx ie the change in y resulting from a small (actually infinitesimal) change in x, as a fraction. Also called rise over run, or slope.
Would be great to do a series going from introducing calculus like this to progressing to haf. Hard🏴🙋♂️
You must be a Catholic?
Awesome video, thank you.
In Dutch we call it differentiation and integration. I remember having learned integration before going to university ( but not in order to study mathematics : ) )
This is better than my math teacher‘s explanation thank you so much
All fine, but if you differentiate y with respect to x, then the form is dy/dx, not dx/dy
i’ve always been interested in advanced math like this but haven’t been able to learn in school. this is because of my own mental health issues aiding in depleting my grades, so i’m unable to learn anything new and am forced to redo simple classes until graduation. i likely won’t be able to attend any college after i graduate. the education system doesn’t seem to actually look out for students from a humanistic standpoint but rather as a way to get kids in and out so that they’ll be able to function as slaves to our economic system.
How did this formula appear? There was no coordinates on your graph. As a matter of fact there was no graph to start with.
Thank you, even old dogs (62) can learn new tricks or calculus.
what an appallingly bad teacher!! He wastes so much time repeating himself with endless waffle and not actually explaining anything, for example what IS a derivative?!
The best youtube recommendation ever
I never learned calculas. I understood the graph, slope, highest point and negative motion of slope. But I could not understand what is d what is f and where from 8 and 9 came practically.
Good explanations. The movie Stand and Deliver is "the story of Jaime Escalante, a high school teacher who successfully inspired his dropout-prone students to learn calculus." I've always been curious if he just taught to a level his students could understand, like your doing here, had tricks or short cuts or just took the time needed to ensure each student understood the material. Any thoughts?
Sorry to go off topic, but my wife and I watched that movie on our Honeymoon in 1989, we were at a cabin in the mountains for a week and I rented us a bunch of movies. I still remember Stand & Deliver, and Gorillas in the Mist after 4 kids and 33 years.
@@Thebigboramyou watched movies on your honeymoon? Maybe I’m crazy but that is nuts.
From basic math conventions, y is always the dependent variable, and equals f(x), and x is the independent variable. This convention is observed to this day in most areas of math ranging from algebra, calculus, statistics, all the way through machine learning to deep learning. Accordingly, a better notation would be y = f(x), dy/dx rather than dx/dy. Especially these days with widespread use of AI/DL/ML, it would be good to train young minds right from the start to use the correct conventions. Also, while this is great, it seems like it could be much more concise. just my .000002
Good catch! I agree with you. the convention is like you stated above. y = f(x), dy/dx rather than dx/dy.
I think you meant to say that y is always the dependent variable, not the independent variable as you wrote in your comment.
I doubt the teacher John knows that the entire engineering is based on dy/dx (gives deflection) and second derivative is d^2y/dx^2 (bending moment) etc.
Schools want us to learn this but not credit score, credit card debt, household financial management, college loan debt. No wonder everyone is in debt up to their eyeballs.
Three whole minutes of gab before getting to the subject. My favorite criticism of youtube.
It would be nice if you have a video on transversals. I'm that kind of guy who enjoys trigonometry, though I am only a first grader :)
Will this be on the test?
Hi!! Thank you so much for this video. I have to take a calculus class for my BA major. I haven’t taken a math class in 5 years. I was scared but watching this video made me realize that it’s not so scary and I can do this! ❤
Three minutes in, you FINALLY get to the problem. WAAAAAY too much time spent promoting yourself, your site, and whatever else I skipped over.
Even though I have published and taught applied quantitative analysis for many years, my knowledge of calculus has been the slope of a horizontal line mentioned in your video. I now know how to create a derivative and find the high point of the parabola. I like your passion for the material and sincerity. However, I suggest you eliminate the irrelevant commentary found throughout the lesson. It is distracting and detracts from your otherwise fine explanation. Thanks for making these videos.
If you master algebra, not just be mediocre at it, you will do very well in pre calc and calc.
There’s a synergy between these skills. I became much better at algebra (and trig) while studying calculus.
Loved algebra but struggled a little with Matrices. Calculus seems more interesting
I'm an eleven year old seeking for more advanced blocks of mathematics that exceed my age level, and this video was a great introduction of calculus.
I’m in the 5th grade (like you probably depending on where you live) I’m also eleven. I want to be a mathematician and I’m trying to get ahead. So I’m watching math videos all day
@@broniesr20percentcoolerthis is excellent guys! Keep up the amazing work 💪🏿
What are we but a calculation, or more precisely, the result of a calculation?
excellent!!! now i understand...
Dy /dx is the derivative of y with respect to x, while dx/ dy is the derivative of x with respect to y. However yoir example shown f'(x ) so it shud be dy/dx
I had a terrific Functions/Trig teacher like this when I went back to refresh... to continue with Cal 1 and Cal 2. Great memory, terrific teacher.
Where is your calculus 1 and 2 courses on your website? Thanks!
In 1966 I was flunking math in the Knavey’s nuclear power school. When I asked for help the instructor told me, “Read the book!” The text book was terrible, it caused me more confusion than anything else. I flunked out out of nuke school. Which, as I learned later, you really had to be really, really weird to enjoy duty on submarines! I could have used a good instructor like yourself, however, I may have become really, really weird.
Most teachers suck. If a student could "just read the book", then there would be no need for teachers.
Could you just do it and quit talking, I'm not interested in your history, just the topic of your video!!!
3 minutes and you're still not into the topic, it's like watching grass grow, or paint dry...
I got bored with the five minute “pay for my course” monologue….goodbye.
13:01. Now I am thoroughly confused. When you’ve got one to the second power, shouldn’t you be multiplying 1×1, which would equal one? You don’t multiply the power by the number? You multiply the number by itself, as many times as the power tells you to? Is this something different?
I completely understand your confusion, John. The rule in finding the derivative is that you multiply the exponent by the coefficient to find the new coefficient. Afterwards, you decrease the original exponent by one to find the new exponent. Here are some examples: 2x^3 becomes 6x^2, 3x^2 becomes 6x, 4x^5 becomes 20x^4, -4x^4 becomes -16x^3, 5x becomes 5, and 3x^-2 becomes -6x^-3. Hope this helps.
@@Generatorman59
Thank you!
@kdjayo1 : He is using a standard formula. If y=x^n then dy/dx= nx^(n-1)
This formula can be derived by methods that are known as ‘first principles’ and requires knowledge of the Binomial Theorem and a concept called ‘limits’.
So frankly this is not the way to teach the ‘first calculus problem’ as he puts it. This is actually a problem on maxima and minima and comes much later in calculus, there are numerous other things you need to know before you get here.
If you really want to understand Calculus, you must learn the first principles. Your fundamentals will be strong then and you can then master this subject.
Could calculus cover irregular lines without any formulas defining it ??
Good video, you right though, you could have just used -b/2a to also find the vertex, but it’s a good representation of beginner calculus.
@ Tyler Michael Hoffman
What do you do when you run across a function like this, f(x) = 8x^8 + 12x^5 - 4x^4 + 10x^3 - 6x + 5? Calculus works every time for both types of functions. -b/2a only works for quadratic equations. This is calculus class. He doesn’t want to use -b/2a. He only wants to teach viewers how to find where a curve’s slope is 0 using only calculus. Now… if this were an algebra class…
Does every calculus problem start with 3 minutes of dribble?
Get to the point then the upsell, check out the RUclips marketing videos.
Offer something before you beg for something.
Blame RUclips. RUclips currently ranks videos based on length so creators have compensated by lengthening their videos to receive a higher ranking. But he could have added more substance instead of babbling on.
This video seems to me is very useful. But, according to this equation, I would like to know about -9 . I didn’t see you mentioning? Thank you for teaching me. Michael Mai
It was the rules in getting the derivatives of a function, -9 is a constant number and according to the rules on getting the derivatives all the constant numbers is equals to zero. Hope you understand it.
@@johnpaulveniegas5443 Technically, isn't it 9x^0 (which = 9), so you take the zero times the 9x and the whoe term becomes zero.
Calculus itself isn't that bad, except they Start it with horrible Limit Theorems, which drives everyone nuts. 😀
You could skip to formulas. But, if you want to understand Calculus, you have to understand limits.
Dy/dx f(x) = -2x -8
FWLIW: The frustration I've always had with 'higher' maths as someone who has no real interest or need but would at least like to understand:
-Here are the concepts - ok, no problem. Please don't muddy things by restating half a dozen different ways, do it right just once.
-Here's a bunch of different ways to write those concepts - ok, but just those required for now would be less confusing.
-Now we'll do a bunch of unexplained manipulations, and there's the result - that might as well have been magic!
It's been my experience that most maths teachers will happily define the concepts multiple ways on the misapprehension that is where their students are confused and more explanation must surely be better rather than more confusing.
They then demonstrate all the ways in which the problem may be stated under the equal misapprehension that their students are as fascinated as themselves - nobody is fascinated by having the expectation that they are about to be made to feel stupid rubbed in their face.
The 'teacher' will then inevitably go on to show the process like a conjurer performing a trick as if said process itself is the most obvious thing in the world, culminating in a result that will seem to be impenetrable magic to most of their students.
The process is never explained, just presented. It is these ill explained nuts and bolts that link the start and finish where all the confusion is to be found.
Very frustrating!
Some advice for budding teachers, especially maths teachers who tend to be those who most desperately need such advice:
-Define the concept(s) required as clearly and succinctly as possible, ONCE, and in only ONE way. Check CAREFULLY that EVERY student gets it and if not CAREFULLY enquire what it is they are struggling with and address those specific issues ONLY.
-Once EVERYBODY is on board introduce any new tools required and ONLY those tools. If it's a maths concept or problem DO NOT introduce multiple notations or methods, stick with ONE and choose the most conceptually straightforward if there is one.
-Make absolutely sure EVERYBODY understands the purpose those new tools, especially their meaning, before ANY further steps are taken.
-Only now is the time to work through illustrations and examples. The following is where 90% of maths teachers loose 90% of their students.
-DO NOT under ANY circumstances run through your examples as if they will be as obvious to your students as they are to you. Many will be instantly turned off as they see the widening gap between their lack of understanding and the impression their poor teacher is giving that it should be easy. Of those few still following along most will have an unnecessarily frustrating devil of a time keeping up. The very few who have no issues will fool you in to thinking all is well - they won't understand what is wrong, destined as they are to regrettably become the next generation of 'teachers'.
-INSTEAD go through EVERY step and symbol in excruciating detail, being very sure that every assumption, implication, and procedure, is unpacked for the clear understanding of all. It is at THIS POINT that NEARLY EVERY maths TEACHER FAILS NEARLY EVERY STUDENT - take your time and do it properly!
-The bells and whistles may be imparted later to those who care and have the ability to grasp them.
this and this and this again . I have no problem with the notation, explained over and over again. I can remember how to magically manipulate the equation. I have no idea of what I am doing because the fundamental concepts underlying the operation are missing.
Just to help... f'(x) = dy/dx, and you forgot the constant (9) derivative, what is zero.
um... dy/dx means change in x related to y where y isn't part of the problem. This seems a little weird to me... f(X) = -x^2 -8x-9... where's the Y?
f(x) represents y. In the same way we could call a function g(x), h(x), etc. They could also represent y.
F(x) is y. With functions, the y-coordinate is a “function” of x, meaning whatever x-value goes into the equation, the equation around it gives the value of y. For example, if the function was f(x)=x+2 then y would equal any x value +2. If x were 3, y would equal 5. And if x were 10 y would equal 12. This is how we conceptualize a changing line, with y being a function of x, or f(x).
So for someone not familiar, when i hear the word "derivative" I think of something derived from another thing. Is that the sense here?
In common language, you’re correct. Derivative means “…arises from…” But in calculus, “derivative” means “the rate at which something changes.”
Your more on talking sample please do directly to the solution, no more prolong talking thank u
You could make math obtainable to anyone interested. If you developed a program that tutored a student while doing problems. The key would be to have the program recognize a mistake and tell the student. But most importantly tell the student what the mistake is and what concept he is missing. I’m a retired lawyer when I went to law school we had very basic computer computers. But we had one program for evidence. In it you would have an issue which you’d rule on if you were wrong it would tell you why. It was basic but powerful. You could really get the hang of it. I think a math teacher and a computer programmer could revolutionize teaching of math. At first I thought it would be good for calculus and it would but it would be great for any level math. Also video type games could be developed to give practical application too.
I wish I knew a math teacher and a programmer who wanted to bring calculus to the world. Calculus is the big separator of intelligent people. Many intelligent people can’t get it. It’s a shame but a constant tutor available would make it doable for any above average intelligent person! 17:42
I had to take business calculus at the beginning of Covid and let me tell you no one knew how to deal with this. We spent two weeks not doing anything and then finally I think the school said just try and get them to pass a class anyway possible and my professor said since we are doing everything online now you get to use your notes you get to help each other and you get to pair up with people taking the final and I passed the class with a B. That was pretty rough.
the graphics are perfect...
Do you have a video to find the value for where the parabola started on the x axis and ends? Like a rocket taking off and landing. Thank you.
Set the equation to 0 and solve for x. For exanple if the equation is y=-x^2+12x-27, then we can see where it crosses the x axis if we set it to 0. So 0=-x^2+12x-27. Now solving for 0 we get x=3, and x=9. That means at x=3, it's on the x axis (floor) going up. And at x=9, it came back down to the ground
Careful! A number of slips of the tongue in this one. Would derivation of the 'rule' be helpful here rather than just saying, "This is the Rule"? Is there a table of rules available for Calculus , like in Geometry ?
Great explanation. Thank you so much
Why then does the first derivative of the volume of a sphere become its area?
I use this math everyday :) Sometimes I forget fundamentals. Appreciate you!
Wow that helped taking classes now and they never said drop the last number for the derivative to make it easier.
Your video is mostly on point except when you say dx/dy, that is NOT the same as dy/dx when taking the derivative in the first way you stated you are taking a function that depends on x but taking its derivative with respect to Y which requires either finding its inverse as a function of Y or implicit differentiation.
Without calculus we wouldn’t have cell phones 📱 or the internet. That is really true. Thank you so much 😊
3:02 is where the vid really starts.
How did he get x=-4, and how did the - trun to + and how he got the 9 and I hav alot more questions
@P0LAR0
He took the derivative of the function f(x) = -x^2 - 8x - 9 which gives the function f’(x) = -2x - 8, which is the derivative function. The derivative of -9 equals 0, so there’s no need or point in writing the 0. You simply write f’(x) = -2x - 8.
He got -4 by setting the derivative f’(x) = -2x - 8 equal to 0, like so, -2x -8 = 0, then he solved for x, which gives -4. Don’t know what you mean when you ask “how did the - turn to +.” Or I should say that I don’t see where that happens here. What do you mean in asking that? And what do you mean in asking “how he got the 9? First, there’s no 9, there’s a -9. And that -9 is simply one of the terms in the equation f(x) = -x^2 - 8x - 9, is all.
Why aren't you teaching at the university level? You're a good teacher. You didn't get your PhD in Mathematics?
Thank you so much!... the way you explain is beyond good, you have a talent for this!... I am taking advanced macroeconomics now, and I started watching this for fun, and I stayed because you are actually putting a picture on my head!
I took calc all the way through differential equations when I was in college. According to K-12 standardized test scores I had great aptitude, but I except for 8th grade algebra when I had a gifted, fabulous teacher I always avoided math because I never really could make it fit together. I thought I was just stupid. Then in my first college math course I got very lucky again and found a teacher that changed my learning life. I had him for college math and algebra but then had to take my first calculus class without him. I dropped it. It was then that I realized a lot of my issues really did have to do with the teachers and the way they taught, and I wasn’t just stupid. But I had finally discovered that I really did love math, so I tried again.
After I transferred to a different college I got another fabulous teacher and stuck with her from Calc 1 through “diffy q’s”. I had to work really hard... I took detailed, voluminous notes, and did all my homework three times, Lol...but I got straight A’s. I also became a successful tutor for a while. Many of my students told me I broke it down better than their teachers and their test scores improved dramatically. I considered going into teaching but decided against it, largely because of the curriculum for educating teachers.
Comprehending math changed my life. It structured my thinking and even helped my writing ability. I was able to write things more clearly because math and specifically calculus had taught me how to pick a problem apart and put it back together to arrive at an orderly, effective solution. Calculus is bar none one of the great brain growing tools of all time.
It’s been 20 years since I finished my DE class. This popped up on my RUclips feed so I decided to give it a watch for a quick, fun refresher. And I gotta say, while I admire the spirit in which this guy is trying to help, if I was a neophyte, struggling student with no previous knowledge of calculus, this wouldn’t have made much sense to me at all. I would have zeroed right out of his Calc class in short order. He’s all over the map. It’s obvious that math and Calc is something that just always kind of made sense to him, and he doesn’t break it down in a way that’s conducive to the kind of structured, almost rote approach that many of us knuckle draggers need to really comprehend and internalize math. The majority of students are knuckle draggers when it comes to math. I can say that because I was one.
One of the things I realized during my math journey in college is that I did not need to grasp the concept being taught immediately in order to be successful. Concepts are important, but it’s not always imperative that they be completely understood immediately in order to achieve success in the classroom. My Calc teacher would sometimes tell us that she was going to teach us the mechanics first and circle back around to the concepts, and also why she was doing it that way for this particular section. It worked! I learned that if I was given a formula and I could memorize it well enough to break a problem down well enough get the right answer for a test, the concept ALWAYS came to me eventually. Sometimes it was sooner, and sometimes it was later. A couple of times the aha moment actually happened during the test while I was working a problem. Lol. The point is that if I could memorize and learn the mechanics well enough to achieve outstanding success on the test, I ALWAYS internalized the concept behind the mechanics at some point.
This guy doesn’t spend enough time on the mechanics, IMO. Rote learning has fallen out of favor, but there’s a huge gap in our education process and our education outcomes because of it. The insistence on complete conceptualization at the expense of the hard work of rote learning is where education in general but math education in particular has been failing our young people for over 40 years. Rote learning is a necessary prerequisite to success for all but a fortunate few. And most of us are never going to go on to be engineers or physicists, so we will never use algebra, trig, or calculus for anything practical in our lives. So if the arcane concepts of slope and area under a curve fade for us over time...that is to say, if the larger concepts fade...its not really any harm. But the restructuring of our brains incurred by learning how to pick a problem apart at the mechanical level and arrive at a correct solution, will never leave us.
That kind of learning is crucial in life. It’s not popular in modern teaching theory and it’s not popular with students cuz the mechanics are hard work, but teachers especially math teachers who don’t ultimately grasp this concept are doing their students a grave disservice.
Just sayin’ in case that helps. This vid gets an A for effort and heart, because it’s in the right place. I think this guy loves his students and he loves math. But it gets just a C for overall effectiveness, which is what really counts.
I think this is an interesting review. It also points to a lot of issues with math teachers. Like you, I have had the good, bad, and ugly when it comes to having a good teacher, especially math.
To this point (for the sake of intelligent conversation), I find myself agreeing with you and simultaneously disagreeing with you (pertaining to me, specifically). In some facets, math was easy. In others, insanely difficult. And not because the math was difficult, but it was too rote; too meaningless; too arbitrary. For me, I needed to understand the concept before the mechanics. I needed to have a reason. There had to be a story. While I agree that a story cannot exist without letters (surely one can not write a story without knowing their letters), it provided a direction for my thinking. Otherwise, there was no use in understanding the letters because the story didn't have meaning anyway; interest was lost.
It seems people that teach math are those that tend to be good at math. In other words, it came natural to them. For those types of people, it is difficult to understand how us knuckledraggers (love that word) are not getting the concepts. Consequently, they teach as they "see" things. And it's really like this in all academia but math is entirely a different language. It demands structure (which as you indicated, one of the very beneficial things about learning math). For example, I teach psychology. My first class gave me terrible reviews, lol. I had no clue why. As it turns out, I talked over everyone's head but did not have a clue until later talking to the students. Why? It is my passion; something that I understand and place together very easily. It was difficult for me (even having experienced this same issue from math teachers) to see that I was doing the same thing to those poor souls. In fact, psychology is one of the reasons I came to appreciate math (as odd as that may seem). I could see the patterns but was lost in the mechanics/language.
Which is why I agree with you about the mechanics being important, but most people do not have the same success from rote memorization (statistically speaking). This is why understanding from your insane work ethic (which is awesome, btw) improved your ability so much; it clicked and you got it! Sadly, I was never taught either sufficiently. I learned more from youtube videos than I ever have from any classroom, though I have had some good teachers years ago. And, it wasn't required for me to learn deep maths, but I have always been the guy who learns things differently, often in reverse of everyone else.
Anyway, I found your comment intriguing. Made me evaluate things....which is the predicate of mathematics, ironically. So thank you.
I think of how many knuckle draggers could have used u as a teacher. I think u would have been one of the great ones.
Uh, the power of uh calculus, uh and….
17:50 he misspoke by saying "negative 7 4" when its "negative 4 7." It was written correctly though, I'm an old fart and still like math. good easy basic, first problem and explanation of such.
calculus make my imagination in calculation getting bigger 😊
In this video, you were saying “dx/dy.” Actually, it is “dy/dx.”
At 1:59...2:01 "My program is very unique".
There is no such a thing as very unique.
Unique is unique. Neither less, nor more . Nor little, nor some, nor very.
Just unique.
OK, so the English language is not you subject.
But repeatedly you've made the biggest howler I've ever seen a maths (yes, mine is British English) teacher guilty of.
"(dx)/(dy)"....that is utter nonsense, unless the y-axis is horizontal and the x-axis vertical.
Need I say more?
Im just watching this so i can get ahead of my class when this is the next lesson
I am a 79 year-old Ivy League Spanish major - (Cornell '67) - never took calculus, and found this video perfectly understandable. The derivative and the calculation of derivative finally make perfect sense to me. I now feel ready to learn more math from TabletClass!