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felt my soul leave my body when she said "there's a reason it normally takes two semesters of university to cover the basics" bruh i'm here trying to teach myself physics within two days in university
+Xoreign That probably would have gotten me a few more points back in high school. But - at least at my university - I never met a professor who took off points when I forgot to add + C.
+Amri Ilias Yeah in the case of an IVP, it is absolutely necessary (and you won't get the correct answer without the constant), but when finding the general integral, my professors really didn't care. They assumed that we knew there was a constant at the end.
+Xoreign The truth is that for every well-defined problem (i.e. which is actually integrable and with well-defined initial conditions) you can always take definite integrals, which takes care of the constants.
being a physics teacher, i was very intrigued when i come across Paul Hewitt. He stresses a lot on learning physics conceptually for beginners, rather than mathematically. It changes the way i see my teaching and learning process for physics. Seeing some of the comments in this and the previous video, it reinforces that point strongly
CK Liang Can't agree with you more. I did physics at A level and the mathematical jargon I had thrown at me at the time created a real barrier to understanding the conceptual relations hidden underneath. Neither Crash Course Astronomy nor even PBS space time throw learners under the bus quite like Crash Course Physics even though they both rely on the language of mathematics.
For all those who are having a little difficulty understanding the maths, don't worry its half a semester of maths in 10 minutes. Make good use of the replay button. Best wishes A fellow Crash Courser
According to wikapedia: Velocity is the derivative of position, Acceleration is the derivative of velocity, Jerk is the derivative of acceleration, Snap is the derivative of jerk, Crackle is the derivative of snap Pop is the derivative of crackle. The scientists who named the last three must have liked their cereal...
I just keep the formulas in a .text and derive as she goes, pausing and rewinding the video constantly, but i do feel that it would have been better to have a precalculus and a calculus crash course before this.
+Mads Andreasen I think you're right. the other crash course series are on knowledge based subjects. maths is a skills subject a skill can only really be developed by repetition so by doing practice questions which doesn't really make for an entertaining "crash course" however I think she did a good job.
+RoarOfDamnation your probably better finding a website that explains it with example questions and step by step solutions, it means you can read over anything until they make sense to you I would find it hard to learn from this with all the colour and animation, it draws your attention away from what you're trying to lean but you should come back to this video afterwards to cement your learning
I would be careful about saying that C is where the curve intersects the vertical axis. This is true for polynomials, but not for, for instance, e^x (where C+1 is the vertical axis intersection). Great series so far. I'm really glad you're doing this.
The only problem with these videos is that the time limit doesn't really allow our teacher to go into WHY these things work the way they do, but they do still give a good general idea of HOW to do it, and that's still pretty good.
+Silver Mirai Fundamental theorem of calculus; Integral from a to b f(x) dx = F(b) - F(a) , F(x) being an anti-derivative. This gets rid of C, saying as the antiderivative of a function at any point will have the same C, so we subtract to cancel it out. What we are left with is the accumulated area under the curve. This is so much more universal than all the rules she talks about, and the second part of the fundamental theorem of calculus states the the derivative of the integral from a to t of f(x) dx = f(t). The second part basically states that the derivative of an integral is the function. Goddamn, they need to show you this theorem on crash course. I guess we'll have to wait until crash course math. :P
+Silver Mirai Also, they never mentioned the anti-derivative of the power rule; if f(x) = x^n , then the anti-derivative F(x) = (x^n+1)/(n+1). Very useful.
We are not the target audience. As she mentioned, this is so far two semesters. So unless you spent two semesters in higher education, nobody expects you to understand it. And neither should you. But if it makes us go back to khans, it has reached it's goal, even with us.
+Silver Mirai Pausing, rewinding and taking moments to think things through helped me a lot. It was especially tough when she would talk about the equations without them being on the screen. I'd recommend taking notes to those who really want to understand and remember these things. Seeing the equations from this and the previous episodes at a moment's notice would help a lot.
+Marrs101 This isn't two semesters, this is only the shortcut to the most basic derivatives and integrals. The two semesters are much harder than this.
I’m a chemist who has been teaching HS physics, and wanted to review some calculus and this video put so much together that will help me go back to explain the basics of position, velocity and acceleration.
I really feel like.... for a *true* and comprehensive intro to physics... this has accelerated much much too fast. I really think the absolute BASICS of physics should've been talked about for like three episodes, using only the most elementary of equations before moving on. This went so far so fast with words that aren't really familiar to most high schoolers and even graduates. I took physics, I took calc. But it's been 10yrs since I've used it. So I _feel_ like a newbie again, but *do* still know the information. And yet this feels like nothing but words and headaches and none of the Crash Course-y "Okay, that probs just made you crossed-eyed, lets break it down in a way that makes sense". And without that, how's this any different from class/textbooks that no one likes and are inaccessible? How we're into full equations, and calculus stuff by episodes two and three without explicitly describing all the fundamentals of physics at _length_, or even how people discovered those things (like in astronomy and even philosophy - though the "who" naturally comes up more there)....is mind-boggling to me. I can't even imagine how people are going to stay engaged even in the way physics is being applied, but given that so many people struggle with physics based on its reliance on math...? Pffft, we went cannonball-style into complex math. That's... not how CC usually goes into things. I feel lost and I KNOW this stuff. Given how much physics is SO huge in life? This just is like a math class with a word problem that looooosely relates life. I'm really surprised a compleeeeetely different approach to this wasn't taken. Usually, with CC we'd at least get a... "Okay. So, you're stuck and only have a window to escape. [quick story about your peril] How on earth are you going to get down? Can you jump without falling? Do you know how high you are? How fast are you going to fall, and would the force break your bones if you tried??? Welp! Physics can help you with that! [cue intro]" Followed by an episode using or teaching about all those things with the story involved from a personal standpoint. This feels like an Episode 10 or 12 kinda content when it comes to Physics. Integrals??? On episode *three*?? We haven't even gotten a hardcore truly deep explanation of basic things like force and velocity and gravity and energy and exertion and units of speed and...all of those! Just a couple quick definitions and then moving along super fast using all those at once together instead of understanding each independently. Why would you even mention Calculus already?? Some people don't even graduate HS with that class EVER? I mean, I get its necessity _in_ physics, but we JUST started. I feel like this just lost a massive amount of the audience who'll be too intimidated to even try to come back. The people that already know and love it and are into this? Yes, ofc they're going to dig it. But CC is about accessibility and giving knowledge to all skill levels. ..while also going into super complex stuff where beginners can pause and digest if they need. But we've not really given them the basics. I'm so confused by the intent here. If 28yo's who have done all this can be overwhelmed and struggle to follow. I have no idea how a high schooler who only just began or hasn't taken physics is going to have any idea what you're talking about. Particularly when, in most schools, they start with algebra 1 or 2, geometry, and maybe get to trig by junior year - unless on an advanced track. Some kids in my HS didn't even get to Physics before graduation (Earth/Space, Bio, and Chem) bc they hadn't had the math required to understand this before graduating. But still there's TONS of physics to be taught and learned and devoured with more simplistic math to start until you work up to higher levels. I know these tools are important to move ahead, but not only did we jump into anything-but-basic material already on episode two, it doesn't feel at all like CC -- just a class... like "do this, cuz this, then, that? get it. good. cuz i do. easy. moving on". *But it also doesn't do Physics and why it's SO fascinating much justice.* I can imagine (and HOPE!) some of that's coming, but the couple introductory episodes should really hook people in to being like omgggg, that's so cool! I didn't know this mattered in all my sports and driving and running and pouring a drink. ..or that I could figure something like that out myself! This really IS everywhere. We just socked em over the head with Calc and probs made them go "ahhhh what the heck physics is awful why would i ever do that or need that or not just get a measuring tape or use google if THIS is what it requires me to figure out?" And, that makes me very very sad. :(
+OurPeanutGallerie I think the problem is that they want to get on to some actual Physics, not do Crash Course Maths, but you can't do any real Physics without calculus. Hence the super fast introduction, "these are the rules of calculus, we're giving them to you so you can at least follow along later". These videos are designed to be used as things teachers can show in class to reinforce learning, not as something that will take you from zero to being able to do it yourself in 4 minutes. They in fact even told us at some point which American Physics course it is based from. If you don't even feel comfortable with the idea of an equation, you really aren't going to understand anything about an introduction to Physics, so it's kind of a no win situation for them. Other Crash Course series have required very little background knowledge in other subjects, so they could get right on with it. Astronomy is a great example, as you can just talk about stars and galaxies and that's cool (at least at the level of the CC series). Same with Biology, Chemistry, Psychology, English Lit, History, you can just get straight into the subject matter at a nice basic level and build up. To actually study Physics requires a good understanding of Maths, otherwise what you're doing is just a pop-science show, and they probably should've done CC Maths before this so that they could just start with basic Physics and build up like in the other series.
+tobywilson -- And, I do understand that. I feel like Math should've been first if they were going to do this. But the thing is? You're suggesting they "want to get on to some real Physics". And I agree and can see that. But, they also do use this in classrooms. High school classrooms, not just college. Most schools? Only the accelerated students take Calc before graduation. And most take it in their senior year (some smartypantses junior). You cannot "get on to some real physics" without calculus. ...and you absolutely cannot teach Calc in a hot minute. So, basically no one in most high schools will ever be prepared for this. And high school Physics teachers won't be teaching THIS kind of Physics. Ours didn't. My college Physics classmates' high schools didn't seem to. I took all advanced classes. I look Physics as a Junior and Calc as a junior. Only twenty kids in my school were ready for Calc that early, so those who were in Physics that you, none of us had _had_ Calc yet. That ENTIRE class was still important, amazing, wild Physics. It was valuable and opened my eyes and other people's eyes. It didn't even TOUCH what has been touched on in episode three. We broke down all the laws of physics and how they're applicable to life, did equations and complicated problem solving. And it wasn't easy. And none of us were stupid. By the time I took a *college* Physics class? Yes, we got to this. But even there, not without TONS of review first. ..bc a lotttt of those kids didn't get physics in high school either. The people who are ready and understand can digest and follow; but those who can't, can't even continue because they weren't given the basics. There were many CC series where the first three were pretty elementary and then we took off super fast. That's perfectly cool. But I worry by episode two, anyone who was interested was like, hell no, I don't even know what she's SAYING, I'm gonna skip this one. And that's sad. With literature and history? They've continued on, done it in chunks. Extra series almost. They've never done any Physics yet. They should've supplied the basics -- material covered in most high schools. And if they wanted to "get on to some real physics" maybe do it in the second half of the series, or do another segment. This just feels like a complete curveball. Absolutely any other series, I can sit down and watch it beginning to end....no matter how long I've been outta school. This doesn't allow that. And most high school teachers aren't teaching any of this either. At least, not until the very end of the course. I was so confused by the approach that I actually dug up my old physics binder out of my closet after my first comment to make sure we didn't do it this way. In a class made for and filled with the top 30 kids in our entire class...? Sure enough, we didn't touch most of this until about 3/4 of the way through. And even then, I'm not sure I would've been able to continue if I hadn't been in Calc at the same time. And remember about half the class had to take Trig instead of Calc that year bc of scheduling...annnd...they struggled. I know they were put between a rock and a hard place. But this feels like a big, big miss. Great for college. Great for maaaaybe maybe a few advanced high schoolers. But unless they dramatically turn into way more accessible presentations? Starting this advanced is only going to serve the AP kids and college kids. ...and, I still worry, intimidate anyone *wanting* to take physics in the future. I know if 15 yo me had seen this? I feel pretty damn sure I woulda nixed Physics so fast. Which, is terribly sad bc Physics is so cool. I know they won't care about my loss of viewership (though I'll probably try back a few times), but I'm still sad for the others that have already checked out. (And hey, I'm someone who even caught the entire Intellectual Property series. I listen to just about anything informative.)
+OurPeanutGallerie I largely agree with you, this series is absolutely pointless and doesn't really explain anything, but I disagree a bit with some of your points. "Most schools? Only the accelerated students take Calc before graduation. And most take it in their senior year (some smartypantses junior). You cannot "get on to some real physics" without calculus. ...and you absolutely cannot teach Calc in a hot minute. So, basically no one in most high schools will ever be prepared for this. And high school Physics teachers won't be teaching THIS kind of Physics. Ours didn't. My college Physics classmates' high schools didn't seem to." "By the time I took a college Physics class? Yes, we got to some of this. But even there, not without TONS of review first." America isn't the whole world. The vast majority of schools teach calculus before university in nearly every country outside of America. By the time you're in university this is most certainly assumed knowledge, there is no review in most countries on whether or not you can use calculus in physics. You won't of managed to get onto a physics course at university if you couldn't. This emphasizes a fair bit how difficult it is to teach a general audience as the background will be so different, even when you're saying "Ok I'm aiming for high school students", because there is such a large variation between different countries on how good/bad their education is. But again I agree with you that this is just stupid. It doesn't really cover anything, just states boring rote learned facts with no actual maths or physics.
BlueCosmology Well that is definitely an important discrepancy I didn't know. And given she, in charge of most the teaching, is *not* American...would have no way to know that and instead assumed this was common grounds. But as meh as it is, CC this far has focused on what's common in American education and then outreached further. Even so, I feel like that could've been completely circumvented for ALL countries and all skill levels to start at the beginning. Explain the theories and laws behind physics and in life applicable ways... then move on. Even doing that for only, hey, 4 episodes and then moving on SUPER fast wouldve made more sense. So that if those new didn't understand they can pause and rewatch the first 3 over and over til they understand while everyone else moves on. This is the just the WEIRDEST starting point and with the _least_ life-applicability. I really really hope after the math parts, the rest of the physics elements at least get some of that unique "why this matters" and not that classroom, here's a problem, solve it, cool bye. Sigh. Still, thanks for the perspective on those points to understand where she might've been coming from...that's important. e Even though, overall I still feel very much the same.
+OurPeanutGallerie I completely agree with you. This is not the right apporach for this series, and they're going to scare a lot of people who were initially interested in physics. And it's not like the US is the only country were students have trouble learning calc. I'm european, and I teach high schoolers part time. Every one of them have been studying physics for one or two years before even starting with calc.
You should seriously consider putting out some lecture notes to accompany these videos. It might help people if they have something to look at and review.
Waaaw, its amazing. I've spent 3 years to refresh my high school derivatives and integrals, and now in only 60 minutes I restored almost all Physics Stuff. Thank you very much
I'm really glad you guys decided to cover derivatives and integrals. My high school physics classes were specifically sans-calculus, but at uni we use calc all the time, so it would be weird to look back at physics without calc.
God, I love the intro music to this series so much it's half the reason I'm watching it. I want a extended version that I can just listen to over and over again.
Wonderful! I'm just about finished with calculus and physics in highschool, but this really put them together beautifully. Can't wait to have a better understanding of them both after my first year of college.
I'm watching these to refresh what I learned in college decades ago. I got A's in Trig and Calc 1 & 2 but I don't think I ever truly understood what I was doing. The area under the curve of speed is position? Oh, yeah, I can picture that now. Thanks! I should've been taught that rather than memorizing all those integration formulas which I couldn't remember now if you put a gun to my head.
This stuff isn't meant to be an in-depth video or a replacement for your high school or college classes. It just covers the basics in a mostly easy to understand way. It's supposed to be a... wait for it... "crash course".
This is wonderful, Thank you. I'm struggling with physics and calc 2 this term (online because of the virus) and I have yet to have the big picture explained to me. It is nice to get a little into why you would want to do this or that and what the integral means. Maybe some of the other videos will help too.
One failed semester of calculus and painfully (and barely) passed one another year. Then 10 years of confusion. Then this video. Then: ahaaaaa... Well, fair enough, I had 10 years to sit on it, but still, where were you Crash Course when I needed you the most?!
A lot of the confusion could ve been prevented by explaining what the power rule is i think: To get the derivative of x^2 it becomes 2x The power number if put in front of the variable. And the power number is taken down a point. So, 2x^3 becomes 6x^2 Because (2*3)x^(3-1)
This course lives up well to the crash course name, but one can't help but feel there should have been a series to introduce us to Calculus before attempting physics. There's no way in such a short time to cover even basic techniques needed to solve basic physical problems such as substitutions, Taylor expansions, and most crucially, generalization from R to R^3 (or R^n). To be honest, without notions of dot and cross product in R^3, it's not even clear the average viewer knows enough trigonometry to perform projections and line integrals. Good job nonetheless. Enough practical knowledge to begin applying it to "nice" physical systems.
***** Feynman is awesome, but he also takes his time explaining things. If nothing else, his lessons are spread out by by interesting personal anecdotes and the like. There's a lot of calculus to learn though. Even if you capture the essence of it in an hour, it'll take a few days to show students the techniques they need for physics.
Being an Mechanical Engineer, I would believe that Maths and Physics is like learning an instrument. It takes time to become good at it, but once you're there you have the opportunity to live a life that is limitlessly engaging and challenging. If you enjoy your job you never work a day in your life.
These are so helpful - thank you! It would be nice, however, to have a practice problem sheet or two for people who are trying to grasp the concept, along with step-by-step solution problems for those of us who like hands on work. Thanks again! :)
For all people studying Physics: It's hard! Calculus is impossible! I'm with you, I'm doing it too! But here's a simple way to understand it better: Read you textbook! Sticky note pages with key equation and conversion tables. Watch all Physics videos, (CC, Khan Academy, etc) And write notes for all of it! Type up a document of notes on google drive or microsoft word showing simple instructions in your own words on how to do these equations and conversions! (And if you're smart, you'll find a way to plug it into your graphing calculator and bring it with you for finals!) Seriously though, if you figure out how to do that, please tell me! Good luck!
If anyone is getting confused, knowing all of the kinematic equations helps a lot. In this problem, since you have the initial velocity of the tennis ball (0 m/s), the acceleration (g), and the time (1.7 s), and you’re trying to find the distance (delta_X), you can use the kinematic equation delta_X = V_initial + 1/2 a t^2 and plug in the values to get your answer. This way, you can solve many (even complex) physics problems, even if you haven’t taken (or don’t understand) calculus! See the physics videos on Khan academy for more info.
The last 2 episodes were basically my intro to calculus uni course. All its missing is line function stuff and that was the whole semester. good stuff.
I had no clue what this video was about a year ago, when I was taking pre-AP, now this is sooooo useful for me (2am, preparing for tomorrow's test). I feel I study calculus BC in my physics class since I only take pre-calc this year hmmm.
OK...I have taken 2 classes in physics and barely passed both. I thought that watching these videos would help me get a better grasp then those classes ever did. I mean Crash Course has helped me a lot with just general knowledge and broadening myself but I still can't wrap my head around the math. X_x
That helps me out a lot too, I think its weird that it helps but it does! Their speaking speed is just not optimal, at the current speed it just sounds like a jumble of information but when it goes faster it seems like the concepts get condensed into a more understandable fashion for one reason or another.
I have to admit that I don't really get the point of these videos because, either you know the maths and thus they are useless, either you don't know and it's way too fast and lacks too much information and explanations to be proprely understood. (I know how much my pupils struggle, even with clear, slow explanations and tons of examples.) I guess the people who don't know how the maths works will just assume that she's right and go with that, trying to understand the pysics in the future episodes. I may be wrong however, so let's wait and see. :)
Well for me it really did help. It helped me to connect what I'm learning at math right now with the physics I'm learning. I did know that there had to be a connection between derivetives and the physics formulas, but I didn't know exactly what. Now I know!
Piffrock taking a Calc class in uni right now, I'm watching this for the different perspective to the material it offers. Who knows what insight may be able to be drawn from hearing/seeing pov's
Oh my god THANK YOU!! I somehow I made it through that first semester of university physics with an A but I didn't comprehend the why of most of the material. Now that I'm about to take Physics 2, I feel like I can finally grasp some of the basics with these explanations.
I always thought that Newtonian physics was just a system of describing how the universe works. You can see how I was blown away when I found out it also had the power of making my head explode.
I'm starting to see a pattern in the comments: all the people cheering this course already know what is being taught. I hope it takes a turn to a more palatable and conceptualized approach soon (like all the other Crash Courses).
+Felds Liscia This is Crash Course physics - unfortunately you can't really avoid basic math. However I agree with you that these first videos are somewhat pointless. The people that already know calculus don't need them and the others won't be able to follow them. Perhaps they should have done a proper Crash Course Math before this one.
+Felds Liscia Yeah I agree with you, it's easy to follow when you know what it talks about, but when it's something new, it goes really fast, and you would really have to pause at every equation to do it yourself, to get to truly understand :I
+orbital1337 Yes, you can avoid math (to a certain degree), this channel is not intended as a way to pass exams but to help understand better the basic concepts of physics. I already know derivatives and integers, but this is not a good way to teach newcomers. This is not how it's been done with philosophy or chemistry. Take newton's laws, for example. You can explain them easily to everybody with almost no maths. They can get to the maths later if they're interested. Hell, I'm subscribed to pbs space time which is considerably harder and they aren't using almost any maths.
+Yyunko _"...you would really have to pause at every equation to do it yourself, to get to truly understand ..."_ That's what you have to do to learn math. Or physics. There are no shortcuts.
The graphics at 3:10 are confusing. I understand calculus, but the way it is explained is poor. Please get a math teacher to work more closely with the graphic designers. While you said, "there is no tidy equation we can use to calculate any integral we want." While that's true, there is a tidy equation for the kinds of curves we are using in this course. Just explain that for the purposes of this course we're going to use simple formulas for modeling positions and velocities, and here are the ways we do derivitaves and integrals on them. Leave the explanation that integrals in general are tough for a crash course calculus.
As much as I love this series, it is incredibly ambitious. Physics is a very complicated subject. You have ten minutes. To dive right into calculus based physics and expect to convey any reasonable understanding is a pipe dream. Anyone who understood this video likely already knows the material. I suggest you guys give an overview and help develop an interest in and a curiosity about basic principles in physics rather than try and teach how to do the calculus in a 10 minute lecture. Peoples heads are going to explode.
Yeah calculus isn't something you can just shoehorn into 2 10 minute videos, crash course calculus would've been a good series to do before this one so people had an understanding going into this one.
Exactly. They're gonna loose part of their audience soon if they keep bombarding people with numbers. It's no use if the only ones who like the vids are the ones who already know it
I think the problem with these two episodes is that so much is presented by fiat... the Newton quotient made a brief appearance in the last video, but slowing down just enough to outline how you get from there to the power rule and the derivative of e^x would have worked wonders (plus, as I said in the comments of that video, giving a geometric argument for the derivative of the sine rather than the very very handwavy "argument" given), as well as a minute or two to go over the connection between antiderivatives and Riemann sums.
Hmm. Since this course is heavily math based maybe it would be useful to put out practice equations so people who are trying to seriously learn along can get a better grasp of the concepts.
+Samantha Stroiazzo I definitely agree. Having only one video on differential and integral calculus each is not nearly enough to be able to learn the subjects.
+Samantha Stroiazzo teaching calculus takes a ton of time, and that's just not the point of this series imo. BUT, luckily, we're on the internet, and there's a place for everything. here on youtube that would be khanacademy, with a playlist of 200! fantastic videos that'll get you through most of those two semesters of university calculus shini mentioned.
+DerUnbekannte Of course. Everyone should know about Khan Academy. BUT, what would be useful is having a few practice worksheets to help ground the ideas only presented here in clear reference to the scenarios given. Shini goes through them fast with the understanding that it will be important but not essential. This is not a course on Calculus but Physics. I just think that having maybe 5 example of the math based exactly on just the math represented would be helpful. A clear 1:1 instead of searching through 200+ videos trying to learn something covered in 1 10 minute video.
please keep this series up. As a mathematics major I find this very helpful. I knew how to find derivatives and integrals but I never knew what they were used for. now I can use this in my physics course!
+aaron mack Jesus... You didn't know what they were for? have you never done any flow rate problems? Volume of a curve rotated around an axis? electrical impulse problems? If you are even past your first calc class I find that hard to believe.
I love these videos keep up the great work ! I wouldn't mind if she spoke not so quickly during parts that require us to think a little about what's been said. On a side note, a beautiful woman into physics, too good to be true.
Nooooooooooooooo!!!!!!!!!! When you start with "integral safe the inverse of derivatives" you rob the fundamental theorem of calculus of its beauty!!! *cries mathematically*
+gyinagal I get that they want to make it simple for the casual viewer to understand, but man, the weight that the fundamental theorm of calculus hold and the way professors hype it up in schools and they way they introduce it is so worth it lol
+gyinagal I learned integration only as the "inverse" operation of derivatives first, then we established the connection with curve area, found that more beautiful!
I like the new show. I am guessing she is showing us calculus so we know where the equations come from. Hopefully she will proceed with algebraic equations and the calculus will make sense as we continue. Knowing a little calculus will be helpful in knowing which equation to choose. Learning the units can also be helpful when picking an equation.
Harrison Wade It hasn't been so far. I haven't been watching crash course economy because I have an econ degree and I know it's intended for people new to it. It should be this way too. I can follow the video because I already know calculus, but those who don't are gonna get lost.
Harrison Wade Then trust me when I say that this is not a good intro to calc. You'll see in a future that she's been missing a lot of stuff. You can't properly explain calculus in 20 min.
Yea I know. I've been trying to memorize the equations while listening to the demonstrations and crunching the numbers. I think all math becomes easier once it's written out in front of you
At 4:40 and 5:44, your claims about the constant of integration only apply to certain cases. Many position functions in physics include expressions beyond simple polynomials. Examples include Euler's number raised to a variable time exponent and periodic motion represented by trigonometric functions. Rather than generalize, I'd mention that the initial value is found by evaluating the expression where time equals zero and that it may differ from the constant of integration.
I started watching this series but have up. I wasnt in the right place. But now, in the last few months I took it upon myself to understand a few things is a mathematical sense. I relearnt my grade 12 maths and learnt some new stuff so I could fathom orbital mechanics and aerodynamics. I can now comfortably calculate the dV for a phasing burn, or the lift and drag of an aircraft. But there's still so much I want to know. Then I remembered Shini with the kickass series on crash course that I gave up on because I got scared of integers. I now get integers, but that was only Ep3. Sorry I'm late. Time to binge and scribble.
I know calculus but I still was confused by watching this video. The pacing is just so off. She's like "lol integrals are the opposite of derivatives right" and then talks about constants for a solid two minutes. y u do this, CC Physics?
+Schindlabua Yeah she should have talked about that in the derivatives video, and just said the rule as, the derivative of a constant C is zero. Then the +C would have been obvious in this video and she wouldn't have had to explain it.
+Schindlabua I personally would have explained vectors first. And then explain calculus much later. Why? Because you can relate vectors to velocity, distance, acceleration etc. Basically vectors actually match up more with the current content that has been covered.
+vdeave No way. This is no way to introduce calc to people new to the idea. Imagine your first calc class was these two videos being projected onto the screen. This series has been pretty bad so far, even if I don't like to recognise it.
jmiquelmb Oh yeah, I agree it's done a pretty bad job at introducing new people to calculus, but I'd think anyone who knew calculus already would follow it.
"And now you have everything there is to know Calculus... no you don't" died there of laughter. A painful and happy laughter. Please also tell us about Residue Theorem - a lot of physics use it... or don't tell us=)
This is better more understandable than my physhic high school teacher. He just gives us the equation. This explains more how the equation was created. Thanks for this course.
I mean I love this, but there are some things about this episode's structure that leave me a little unsatisfied. For example, if I were new to the concept of calculus, I'd have liked to be walked through the entire derivation and integration process a couple of times as seen on the same numbers throughout, whereas the last two episodes have only been showing separate individual steps of each, with different numbers at each step. This makes it harder to visualize, at least that's how I'd feel if I were new to this. Moreover, this part ( 6:30 ) bothered me. Yes, I know this 9,81 is the Earth's gravitational acceleration, but someone who's completely new to this will be left wondering if they missed a step, because the number 9,81 seems to come out of nowhere for now. Besides, you guys in the comments, remember that in some countries calculus is not taught at schools, or is only taught in a very small scope. For Americans it may be a review, but for many foreigners it's a whole new thing to get used to.
Yeah, I mean I think it would make more sense to introduce the physical formulas first, just to give the students an idea of the possible applications for calculus, and then talk about the math behind all that.
+Geekminer It's better to save vectors until you get to 2-D and 3-D motion. They would just be confusing (assuming you had never seen then before) when you are only dealing with 1-D motion.
+corhydron111 I disagree. You don't learn physics by memorizing formulas. You learn physics by understanding where the formulas come from, and to do that you need calculus.
Michael Sommers I don't think Crash Course's videos should be used to learn material they're covering. It should be used as a reference or revision. Crash Course mainly caters to those who a reviewing a subject not learning it.
The graphic at 4:50 is misleading. The constant doesn't always equal the y-intercept, as the picture shows. This proposition is only certain for polynomials; a function such as e^x doesn't do this.
This seems more complicated than it needs to be. You genuinely don't care what value your speed is at any given time, what you need is the speed function. You also don't need to drag around C all the way back into the motion function. You can resolve it as soon as you find the speed function. A single constant is trivial to resolve as long as you know the function value for a specific value of the variable. We know the speed was 0 at time 0, so C is 0. Integrate the result again and you get the motion function with another constant. We know that the location was 0 at time 0, so you can weed that out, as well. f(0) = 0 f'(0) = 0 f''(t) = 9.81 f(1.7) = ? f'(t) = ∫f''(t)*dt = ∫9.81*dt = 9.81t + C f'(0) = 0 9.81*0 + C = 0 C = 0 => f'(t) = 9.81t f(t) = ∫f'(t)dt = ∫9.81t*dt = 1/2(9.81)t^2 + C = 4.905t^2 + C f(0) = 0 4.905*0^2 + C = 0 C = 0 => f(t) = 4.905t^2 f(1.7) = 4.905*(1.7)^2 = 4.905*2.89 = 14.17545 Mind you, all of this is assuming our graph is upside-down. With cartesian coordinates, g would actually be -9.81, since it would accelerate items "down" while the y axis (which is what we're using here to determine "height") is positive in the "up" direction and negative in the "down" direction. Technically, the "height" of our window from the origin point of "us" would be -14.17545m, meaning the ball ended up ~14 meters below us.
I consider myself a reasonably smart fellow, but this video, same as the previous one, reminded me that maths is the one thing I have real trouble understanding. At least at this pace.
+Bryan Coronel Be worried. Be very worried. Calc isn't algebra. after several years of calc and algebra and actually using some of it (like maybe 10%) Calc and algebra are just two completely different beasts. If you do really well in algebra (like myself) you'll struggle in calc. If you do really well at Calc (like a very good friend of mine) you'll struggle at algebra. Don't know why it works like that but it just does. It's just a totally different way of looking at math. I switched everything up and said screw math, math and went statistics. which is still math, but we also have to interpret our findings. Always take a stat class if you can. calc is great. but I'd honestly suggest ap stat if you can take that instead. it'll be boring but once the easy stuff is out of the way then you can get into relevant data analysis and regression and that's what will set you apart from anyone else looking for jobs. You know and understand statistics.
I can appreciate the disclaimer at 9:10, but it seems that the fact that it wasn't explicitly asserted beforehand that one cannot learn calculus from two 10-min videos alone is causing grief for a lot of viewers. I've had previous exposure to calculus and can say that these videos really have strengthened my understanding of it. I also understand why the subject was only scratched and not left out of the physics course entirely. I just think that the audience needed a stronger reminder that if they really want to master calculus and physics, they'll have to treat these videos as introductory/supplementary material. Then again, it is CRASH Course. Maybe people should know better.
+KVergara Unlike the history video series or economic series these videos are very difficult to follow and only apply to a very small audience. One that has been introduced to calculus but not gone too far in.
We made quiz questions to help you review the content in this episode! Find them on the free Crash Course App!
Download it here for Apple Devices: apple.co/3d4eyZo
Download it here for Android Devices: bit.ly/3TW06aP
felt my soul leave my body when she said "there's a reason it normally takes two semesters of university to cover the basics" bruh i'm here trying to teach myself physics within two days in university
"If you watched our last episode, you now know everything about derivatives and how to use them."
That is a bold assumption, I must say.
on calculus tests I used to add "+ C" to my name at the top, to remember to add it for any integration problems. haha
+Xoreign That probably would have gotten me a few more points back in high school. But - at least at my university - I never met a professor who took off points when I forgot to add + C.
+Tyler Snell But if you forget it in a physics problem and there is initiale velocity/position...
+Amri Ilias Yeah in the case of an IVP, it is absolutely necessary (and you won't get the correct answer without the constant), but when finding the general integral, my professors really didn't care. They assumed that we knew there was a constant at the end.
+Xoreign The truth is that for every well-defined problem (i.e. which is actually integrable and with well-defined initial conditions) you can always take definite integrals, which takes care of the constants.
Q: Why do they never serve beer at a math party?
A: Because you can't drink and derive...
:D (sorry I just had to) :D
Lol :D
+Jim James that's a math teacher joke right there :D
-Nick J.
you gotta know your limits :P
BlueHawkPictures LOL!
+Jim James GET OUT!!! *throws tomatoes*
being a physics teacher, i was very intrigued when i come across Paul Hewitt. He stresses a lot on learning physics conceptually for beginners, rather than mathematically. It changes the way i see my teaching and learning process for physics. Seeing some of the comments in this and the previous video, it reinforces that point strongly
CK Liang Can't agree with you more. I did physics at A level and the mathematical jargon I had thrown at me at the time created a real barrier to understanding the conceptual relations hidden underneath. Neither Crash Course Astronomy nor even PBS space time throw learners under the bus quite like Crash Course Physics even though they both rely on the language of mathematics.
For all those who are having a little difficulty understanding the maths, don't worry its half a semester of maths in 10 minutes. Make good use of the replay button.
Best wishes
A fellow Crash Courser
According to wikapedia:
Velocity is the derivative of position,
Acceleration is the derivative of velocity,
Jerk is the derivative of acceleration,
Snap is the derivative of jerk,
Crackle is the derivative of snap
Pop is the derivative of crackle.
The scientists who named the last three must have liked their cereal...
lolol
It gets better!
The derivative of jerk is snap
The derivative of snap is crackle
The derivative of crackle is pop
I could go on!
+Adraria8 I haven't seen an ad for rice crispies in decades.
+TheGamingWhovian he even said that
Physics always connected with maty
Just do CrashCourse: Calculus
+Tomas Morales THIS HAS TO BE A THING
+
No, they'll ruin it with that speed.
Agree, this isn‘t really working. Still waiting on math crash course topics.
@@studentcalling9336 3Blue1Brown though? Probably the best intro to calc playlist out there.
i cant imagine how the avg viewer with no prior knowledge of calculus would actually understand calculus just by watching this video
I just keep the formulas in a .text and derive as she goes, pausing and rewinding the video constantly, but i do feel that it would have been better to have a precalculus and a calculus crash course before this.
+Mads Andreasen I think you're right. the other crash course series are on knowledge based subjects. maths is a skills subject a skill can only really be developed by repetition so by doing practice questions which doesn't really make for an entertaining "crash course" however I think she did a good job.
they could have gone algebra only like ap physics that would be easy
+RoarOfDamnation your probably better finding a website that explains it with example questions and step by step solutions, it means you can read over anything until they make sense to you I would find it hard to learn from this with all the colour and animation, it draws your attention away from what you're trying to lean but you should come back to this video afterwards to cement your learning
+Mads Andreasen yeah, i know
I made the mistake of watching this at 1.5x speed to save some time.
big mistake
Sounds like your wife is yelling at you. Lol
Oh it can't be that bad.
*tries
I retract my previous statement.
I watched at 2x...
Then you are not a human being
I'm starting to wonder if there should be an entire crashcourse calculus before a crashcourse physics now...
+Cuckoo Phendula There are only a couple more "Math Heavy" episodes coming. We can keep heading back to these for reference. :)
-Nick J.
I have an integral test tomorrow. I came here to procrastinate, but you got me.
Instead of the last two videos, CC should've redirected everyone to 3blue1brown's essence of calculus series
I learned more with this video than with my 2 semesters at the university. We need a CrashCourse on Calculus! This was awesome; thanks!
The graphic at 2:35 is wrong, it should say x=t^2 is the integral of v=2t.
true
+ c..... Never forget the plus c
+Mistic Mike never forget the dx ....
It's definitely wrong, but I think it was meant to be: x=2t is the derivative of v=t^2
+deeppurplehaze95 function!
I would be careful about saying that C is where the curve intersects the vertical axis. This is true for polynomials, but not for, for instance, e^x (where C+1 is the vertical axis intersection).
Great series so far. I'm really glad you're doing this.
Never have i been more excited to find out how tall a window is
Calculus is integral to physics.
I'll show myself out.
The only problem with these videos is that the time limit doesn't really allow our teacher to go into WHY these things work the way they do, but they do still give a good general idea of HOW to do it, and that's still pretty good.
don't understand shit, back to khanacademy, when I learn on my own pace, I understand everything
+Silver Mirai Fundamental theorem of calculus; Integral from a to b f(x) dx = F(b) - F(a) , F(x) being an anti-derivative. This gets rid of C, saying as the antiderivative of a function at any point will have the same C, so we subtract to cancel it out. What we are left with is the accumulated area under the curve. This is so much more universal than all the rules she talks about, and the second part of the fundamental theorem of calculus states the the derivative of the integral from a to t of f(x) dx = f(t). The second part basically states that the derivative of an integral is the function. Goddamn, they need to show you this theorem on crash course. I guess we'll have to wait until crash course math. :P
+Silver Mirai Also, they never mentioned the anti-derivative of the power rule; if f(x) = x^n , then the anti-derivative F(x) = (x^n+1)/(n+1). Very useful.
We are not the target audience. As she mentioned, this is so far two semesters. So unless you spent two semesters in higher education, nobody expects you to understand it. And neither should you. But if it makes us go back to khans, it has reached it's goal, even with us.
+Silver Mirai Pausing, rewinding and taking moments to think things through helped me a lot. It was especially tough when she would talk about the equations without them being on the screen.
I'd recommend taking notes to those who really want to understand and remember these things. Seeing the equations from this and the previous episodes at a moment's notice would help a lot.
+Marrs101 This isn't two semesters, this is only the shortcut to the most basic derivatives and integrals. The two semesters are much harder than this.
I’m a chemist who has been teaching HS physics, and wanted to review some calculus and this video put so much together that will help me go back to explain the basics of position, velocity and acceleration.
literally 10 minutes of this is a billion times better than an hour of listening to my prof try and explain it
I really feel like.... for a *true* and comprehensive intro to physics... this has accelerated much much too fast. I really think the absolute BASICS of physics should've been talked about for like three episodes, using only the most elementary of equations before moving on. This went so far so fast with words that aren't really familiar to most high schoolers and even graduates.
I took physics, I took calc. But it's been 10yrs since I've used it. So I _feel_ like a newbie again, but *do* still know the information. And yet this feels like nothing but words and headaches and none of the Crash Course-y "Okay, that probs just made you crossed-eyed, lets break it down in a way that makes sense". And without that, how's this any different from class/textbooks that no one likes and are inaccessible?
How we're into full equations, and calculus stuff by episodes two and three without explicitly describing all the fundamentals of physics at _length_, or even how people discovered those things (like in astronomy and even philosophy - though the "who" naturally comes up more there)....is mind-boggling to me.
I can't even imagine how people are going to stay engaged even in the way physics is being applied, but given that so many people struggle with physics based on its reliance on math...? Pffft, we went cannonball-style into complex math. That's... not how CC usually goes into things. I feel lost and I KNOW this stuff. Given how much physics is SO huge in life? This just is like a math class with a word problem that looooosely relates life. I'm really surprised a compleeeeetely different approach to this wasn't taken. Usually, with CC we'd at least get a... "Okay. So, you're stuck and only have a window to escape. [quick story about your peril] How on earth are you going to get down? Can you jump without falling? Do you know how high you are? How fast are you going to fall, and would the force break your bones if you tried??? Welp! Physics can help you with that! [cue intro]" Followed by an episode using or teaching about all those things with the story involved from a personal standpoint.
This feels like an Episode 10 or 12 kinda content when it comes to Physics. Integrals??? On episode *three*?? We haven't even gotten a hardcore truly deep explanation of basic things like force and velocity and gravity and energy and exertion and units of speed and...all of those! Just a couple quick definitions and then moving along super fast using all those at once together instead of understanding each independently. Why would you even mention Calculus already?? Some people don't even graduate HS with that class EVER? I mean, I get its necessity _in_ physics, but we JUST started. I feel like this just lost a massive amount of the audience who'll be too intimidated to even try to come back. The people that already know and love it and are into this? Yes, ofc they're going to dig it. But CC is about accessibility and giving knowledge to all skill levels. ..while also going into super complex stuff where beginners can pause and digest if they need. But we've not really given them the basics. I'm so confused by the intent here.
If 28yo's who have done all this can be overwhelmed and struggle to follow. I have no idea how a high schooler who only just began or hasn't taken physics is going to have any idea what you're talking about. Particularly when, in most schools, they start with algebra 1 or 2, geometry, and maybe get to trig by junior year - unless on an advanced track. Some kids in my HS didn't even get to Physics before graduation (Earth/Space, Bio, and Chem) bc they hadn't had the math required to understand this before graduating. But still there's TONS of physics to be taught and learned and devoured with more simplistic math to start until you work up to higher levels.
I know these tools are important to move ahead, but not only did we jump into anything-but-basic material already on episode two, it doesn't feel at all like CC -- just a class... like "do this, cuz this, then, that? get it. good. cuz i do. easy. moving on". *But it also doesn't do Physics and why it's SO fascinating much justice.* I can imagine (and HOPE!) some of that's coming, but the couple introductory episodes should really hook people in to being like omgggg, that's so cool! I didn't know this mattered in all my sports and driving and running and pouring a drink. ..or that I could figure something like that out myself! This really IS everywhere. We just socked em over the head with Calc and probs made them go "ahhhh what the heck physics is awful why would i ever do that or need that or not just get a measuring tape or use google if THIS is what it requires me to figure out?" And, that makes me very very sad. :(
+OurPeanutGallerie
I think the problem is that they want to get on to some actual Physics, not do Crash Course Maths, but you can't do any real Physics without calculus. Hence the super fast introduction, "these are the rules of calculus, we're giving them to you so you can at least follow along later". These videos are designed to be used as things teachers can show in class to reinforce learning, not as something that will take you from zero to being able to do it yourself in 4 minutes. They in fact even told us at some point which American Physics course it is based from. If you don't even feel comfortable with the idea of an equation, you really aren't going to understand anything about an introduction to Physics, so it's kind of a no win situation for them. Other Crash Course series have required very little background knowledge in other subjects, so they could get right on with it. Astronomy is a great example, as you can just talk about stars and galaxies and that's cool (at least at the level of the CC series). Same with Biology, Chemistry, Psychology, English Lit, History, you can just get straight into the subject matter at a nice basic level and build up. To actually study Physics requires a good understanding of Maths, otherwise what you're doing is just a pop-science show, and they probably should've done CC Maths before this so that they could just start with basic Physics and build up like in the other series.
+tobywilson -- And, I do understand that. I feel like Math should've been first if they were going to do this. But the thing is? You're suggesting they "want to get on to some real Physics". And I agree and can see that. But, they also do use this in classrooms. High school classrooms, not just college.
Most schools? Only the accelerated students take Calc before graduation. And most take it in their senior year (some smartypantses junior). You cannot "get on to some real physics" without calculus. ...and you absolutely cannot teach Calc in a hot minute. So, basically no one in most high schools will ever be prepared for this. And high school Physics teachers won't be teaching THIS kind of Physics. Ours didn't. My college Physics classmates' high schools didn't seem to.
I took all advanced classes. I look Physics as a Junior and Calc as a junior. Only twenty kids in my school were ready for Calc that early, so those who were in Physics that you, none of us had _had_ Calc yet. That ENTIRE class was still important, amazing, wild Physics. It was valuable and opened my eyes and other people's eyes. It didn't even TOUCH what has been touched on in episode three. We broke down all the laws of physics and how they're applicable to life, did equations and complicated problem solving. And it wasn't easy. And none of us were stupid.
By the time I took a *college* Physics class? Yes, we got to this. But even there, not without TONS of review first. ..bc a lotttt of those kids didn't get physics in high school either. The people who are ready and understand can digest and follow; but those who can't, can't even continue because they weren't given the basics. There were many CC series where the first three were pretty elementary and then we took off super fast. That's perfectly cool. But I worry by episode two, anyone who was interested was like, hell no, I don't even know what she's SAYING, I'm gonna skip this one. And that's sad.
With literature and history? They've continued on, done it in chunks. Extra series almost. They've never done any Physics yet. They should've supplied the basics -- material covered in most high schools. And if they wanted to "get on to some real physics" maybe do it in the second half of the series, or do another segment. This just feels like a complete curveball. Absolutely any other series, I can sit down and watch it beginning to end....no matter how long I've been outta school. This doesn't allow that. And most high school teachers aren't teaching any of this either. At least, not until the very end of the course. I was so confused by the approach that I actually dug up my old physics binder out of my closet after my first comment to make sure we didn't do it this way. In a class made for and filled with the top 30 kids in our entire class...? Sure enough, we didn't touch most of this until about 3/4 of the way through. And even then, I'm not sure I would've been able to continue if I hadn't been in Calc at the same time. And remember about half the class had to take Trig instead of Calc that year bc of scheduling...annnd...they struggled.
I know they were put between a rock and a hard place. But this feels like a big, big miss. Great for college. Great for maaaaybe maybe a few advanced high schoolers. But unless they dramatically turn into way more accessible presentations? Starting this advanced is only going to serve the AP kids and college kids. ...and, I still worry, intimidate anyone *wanting* to take physics in the future. I know if 15 yo me had seen this? I feel pretty damn sure I woulda nixed Physics so fast. Which, is terribly sad bc Physics is so cool.
I know they won't care about my loss of viewership (though I'll probably try back a few times), but I'm still sad for the others that have already checked out. (And hey, I'm someone who even caught the entire Intellectual Property series. I listen to just about anything informative.)
+OurPeanutGallerie I largely agree with you, this series is absolutely pointless and doesn't really explain anything, but I disagree a bit with some of your points.
"Most schools? Only the accelerated students take Calc before graduation. And most take it in their senior year (some smartypantses junior). You cannot "get on to some real physics" without calculus. ...and you absolutely cannot teach Calc in a hot minute. So, basically no one in most high schools will ever be prepared for this. And high school Physics teachers won't be teaching THIS kind of Physics. Ours didn't. My college Physics classmates' high schools didn't seem to."
"By the time I took a college Physics class? Yes, we got to some of this. But even there, not without TONS of review first."
America isn't the whole world. The vast majority of schools teach calculus before university in nearly every country outside of America. By the time you're in university this is most certainly assumed knowledge, there is no review in most countries on whether or not you can use calculus in physics. You won't of managed to get onto a physics course at university if you couldn't.
This emphasizes a fair bit how difficult it is to teach a general audience as the background will be so different, even when you're saying "Ok I'm aiming for high school students", because there is such a large variation between different countries on how good/bad their education is.
But again I agree with you that this is just stupid. It doesn't really cover anything, just states boring rote learned facts with no actual maths or physics.
BlueCosmology Well that is definitely an important discrepancy I didn't know. And given she, in charge of most the teaching, is *not* American...would have no way to know that and instead assumed this was common grounds. But as meh as it is, CC this far has focused on what's common in American education and then outreached further. Even so, I feel like that could've been completely circumvented for ALL countries and all skill levels to start at the beginning. Explain the theories and laws behind physics and in life applicable ways... then move on. Even doing that for only, hey, 4 episodes and then moving on SUPER fast wouldve made more sense. So that if those new didn't understand they can pause and rewatch the first 3 over and over til they understand while everyone else moves on. This is the just the WEIRDEST starting point and with the _least_ life-applicability.
I really really hope after the math parts, the rest of the physics elements at least get some of that unique "why this matters" and not that classroom, here's a problem, solve it, cool bye. Sigh.
Still, thanks for the perspective on those points to understand where she might've been coming from...that's important. e
Even though, overall I still feel very much the same.
+OurPeanutGallerie I completely agree with you. This is not the right apporach for this series, and they're going to scare a lot of people who were initially interested in physics. And it's not like the US is the only country were students have trouble learning calc. I'm european, and I teach high schoolers part time. Every one of them have been studying physics for one or two years before even starting with calc.
You should seriously consider putting out some lecture notes to accompany these videos. It might help people if they have something to look at and review.
+Michael Sommers uh... why not take your own notes while watching?
+Hugo Fontes
You could, of course, but prepared notes could expand on what was in the video, and could include problems and solutions.
Your my new second favorite crash course host!
You're*
whs your 1#
*Who's
Who's the first?
She's the sexiest
Waaaw, its amazing. I've spent 3 years to refresh my high school derivatives and integrals, and now in only 60 minutes I restored almost all Physics Stuff. Thank you very much
I'm really glad you guys decided to cover derivatives and integrals. My high school physics classes were specifically sans-calculus, but at uni we use calc all the time, so it would be weird to look back at physics without calc.
God, I love the intro music to this series so much it's half the reason I'm watching it. I want a extended version that I can just listen to over and over again.
Not gonna lie I'm a senior Mechanical Engineering major and I found this hard to follow.
Wonderful! I'm just about finished with calculus and physics in highschool, but this really put them together beautifully. Can't wait to have a better understanding of them both after my first year of college.
This is the best way I've been taught integrals
Same
My favourite simple integral in physics explains conservation of momentum. Since F=m*dv/dt, it follows that the integral of Fdt=the integral of mdv.
You go through this very fast and in to much detail. I'm an engineering student and I only keep up because I know this.
I'm watching these to refresh what I learned in college decades ago. I got A's in Trig and Calc 1 & 2 but I don't think I ever truly understood what I was doing. The area under the curve of speed is position? Oh, yeah, I can picture that now. Thanks! I should've been taught that rather than memorizing all those integration formulas which I couldn't remember now if you put a gun to my head.
2:34 shouldn't this be the other way around?
This stuff isn't meant to be an in-depth video or a replacement for your high school or college classes. It just covers the basics in a mostly easy to understand way.
It's supposed to be a... wait for it... "crash course".
This is wonderful, Thank you. I'm struggling with physics and calc 2 this term (online because of the virus) and I have yet to have the big picture explained to me. It is nice to get a little into why you would want to do this or that and what the integral means. Maybe some of the other videos will help too.
One failed semester of calculus and painfully (and barely) passed one another year. Then 10 years of confusion. Then this video. Then: ahaaaaa... Well, fair enough, I had 10 years to sit on it, but still, where were you Crash Course when I needed you the most?!
A lot of the confusion could ve been prevented by explaining what the power rule is i think:
To get the derivative of x^2 it becomes 2x
The power number if put in front of the variable. And the power number is taken down a point.
So, 2x^3 becomes 6x^2
Because (2*3)x^(3-1)
+HexerPsy There was a video previous to this, they are numbered you know, that explains this rule.
+HexerPsy That was already explained.
+HexerPsy Thank you! Very helpful!
"And that is everything you need to know about calculus"
That was the funniest shit I have ever heard in my life
This course lives up well to the crash course name, but one can't help but feel there should have been a series to introduce us to Calculus before attempting physics. There's no way in such a short time to cover even basic techniques needed to solve basic physical problems such as substitutions, Taylor expansions, and most crucially, generalization from R to R^3 (or R^n). To be honest, without notions of dot and cross product in R^3, it's not even clear the average viewer knows enough trigonometry to perform projections and line integrals.
Good job nonetheless. Enough practical knowledge to begin applying it to "nice" physical systems.
***** Feynman is awesome, but he also takes his time explaining things. If nothing else, his lessons are spread out by by interesting personal anecdotes and the like. There's a lot of calculus to learn though. Even if you capture the essence of it in an hour, it'll take a few days to show students the techniques they need for physics.
Can you recommend a good way to efficiently learn calculus in an audio visual way? i.e. series of talks or videos like these.
Read a book. Spivak is pretty good.
Being an Mechanical Engineer, I would believe that Maths and Physics is like learning an instrument. It takes time to become good at it, but once you're there you have the opportunity to live a life that is limitlessly engaging and challenging. If you enjoy your job you never work a day in your life.
You lost me at :10
+kounsucks lasted 10 times longer than me
I like it, I didn't know nothing about it and I know that just watching I won't be able to take it easy.
I'll keep track of this series.
I used to know all this. How did I not understand anything from this video?
+Zoy Jablabber well i think she went super slow, but i supose tha that if you never have hear of thins can be tricky
Derivative is the measurement of change! I was starting at a paper for ten minutes last episode trying to figure that out
These are so helpful - thank you! It would be nice, however, to have a practice problem sheet or two for people who are trying to grasp the concept, along with step-by-step solution problems for those of us who like hands on work. Thanks again! :)
This is going to be the best crash course since Astronomy and Chemistry
Don't forget about philosophy
Best? History was the best. here we're doing some boring easy algebra
Olivier G. It's just the beginning
_ baktom Yeah but then don't say "this is the best course since [...]"
Am totally in love with her hahahahha
For all people studying Physics:
It's hard! Calculus is impossible! I'm with you, I'm doing it too! But here's a simple way to understand it better:
Read you textbook! Sticky note pages with key equation and conversion tables. Watch all Physics videos, (CC, Khan Academy, etc)
And write notes for all of it! Type up a document of notes on google drive or microsoft word showing simple instructions in your own words on how to do these equations and conversions! (And if you're smart, you'll find a way to plug it into your graphing calculator and bring it with you for finals!) Seriously though, if you figure out how to do that, please tell me!
Good luck!
If anyone is getting confused, knowing all of the kinematic equations helps a lot. In this problem, since you have the initial velocity of the tennis ball (0 m/s), the acceleration (g), and the time (1.7 s), and you’re trying to find the distance (delta_X), you can use the kinematic equation delta_X = V_initial + 1/2 a t^2 and plug in the values to get your answer. This way, you can solve many (even complex) physics problems, even if you haven’t taken (or don’t understand) calculus! See the physics videos on Khan academy for more info.
Nice! I personally find that integrals were better explained than derivatives. Good job :)
The last 2 episodes were basically my intro to calculus uni course. All its missing is line function stuff and that was the whole semester. good stuff.
YES MATE. CALCULUS ON THE FIRST TWO EPS. THATS WHAT IM TALKING ABOUT. PHYSICS BOIS
I had no clue what this video was about a year ago, when I was taking pre-AP, now this is sooooo useful for me (2am, preparing for tomorrow's test). I feel I study calculus BC in my physics class since I only take pre-calc this year hmmm.
She just explained the whole integrals chapter 🌚❤
OK...I have taken 2 classes in physics and barely passed both. I thought that watching these videos would help me get a better grasp then those classes ever did. I mean Crash Course has helped me a lot with just general knowledge and broadening myself but I still can't wrap my head around the math. X_x
just lower your speed else everything is very good
sit through it on double time, and try again reg speed, it'll seem like cake.
seriously, I had a hard time focusing on her videos but speeding it up to 1.5x actually helped me focus somehow
It's way too slow.
That helps me out a lot too, I think its weird that it helps but it does! Their speaking speed is just not optimal, at the current speed it just sounds like a jumble of information but when it goes faster it seems like the concepts get condensed into a more understandable fashion for one reason or another.
I am fine with this speed i dont get why do people think its to fast
I have to admit that I don't really get the point of these videos because, either you know the maths and thus they are useless, either you don't know and it's way too fast and lacks too much information and explanations to be proprely understood. (I know how much my pupils struggle, even with clear, slow explanations and tons of examples.)
I guess the people who don't know how the maths works will just assume that she's right and go with that, trying to understand the pysics in the future episodes.
I may be wrong however, so let's wait and see. :)
+Piffrock I've had the same reactions. Too fast to understand/learn... so kind of a waste.
Well for me it really did help. It helped me to connect what I'm learning at math right now with the physics I'm learning. I did know that there had to be a connection between derivetives and the physics formulas, but I didn't know exactly what. Now I know!
I think this course is only good when you need to refresh yourself... a few years after university... (for me it's 11 years... ;) )
Piffrock taking a Calc class in uni right now, I'm watching this for the different perspective to the material it offers. Who knows what insight may be able to be drawn from hearing/seeing pov's
it's to understand how math relates to physics, it's helpful to me as i had a semester of calculus and now i'm taking Mecanics
Oh my god THANK YOU!! I somehow I made it through that first semester of university physics with an A but I didn't comprehend the why of most of the material. Now that I'm about to take Physics 2, I feel like I can finally grasp some of the basics with these explanations.
Who else feels stupid having watched this?
+watcherjohnny Well I could've learned this stuff in high school but I chose the easy way out.
+The Gray Pet Well I could've learned this stuff in Freshman year but nobody ever told me how easy it was.
+watcherjohnny I feel -mentally- challenged but can manage if I take my time. Really take my time.
I don't necessarily feel stupid, just a bit frustrated and overwhelmed because I don't know any of this.
+Kenneth Yanez if you havent taken calculus... then how could you have learned this?
I found this video very helpful, i didn't know that velocity and acceleration could be related to position in this way, 10/10.
I always thought that Newtonian physics was just a system of describing how the universe works. You can see how I was blown away when I found out it also had the power of making my head explode.
2:42 The tidy equation to calculate any integral you want is called "the limit definition of a definite integral".
I'm starting to see a pattern in the comments: all the people cheering this course already know what is being taught.
I hope it takes a turn to a more palatable and conceptualized approach soon (like all the other Crash Courses).
+Felds Liscia This is Crash Course physics - unfortunately you can't really avoid basic math. However I agree with you that these first videos are somewhat pointless. The people that already know calculus don't need them and the others won't be able to follow them. Perhaps they should have done a proper Crash Course Math before this one.
+Felds Liscia Yeah I agree with you, it's easy to follow when you know what it talks about, but when it's something new, it goes really fast, and you would really have to pause at every equation to do it yourself, to get to truly understand :I
+orbital1337 Yes, you can avoid math (to a certain degree), this channel is not intended as a way to pass exams but to help understand better the basic concepts of physics. I already know derivatives and integers, but this is not a good way to teach newcomers. This is not how it's been done with philosophy or chemistry. Take newton's laws, for example. You can explain them easily to everybody with almost no maths. They can get to the maths later if they're interested. Hell, I'm subscribed to pbs space time which is considerably harder and they aren't using almost any maths.
+Yyunko _"...you would really have to pause at every equation to do it yourself, to get to truly understand ..."_
That's what you have to do to learn math. Or physics. There are no shortcuts.
Michael Sommers The format is not adecuate for the subject they're trying to explain. That's not how it's been done in crash course chemistry.
OMG this is so great! Thank you for making this short and sweet. The graphics are wonderful!
The graphics at 3:10 are confusing. I understand calculus, but the way it is explained is poor. Please get a math teacher to work more closely with the graphic designers.
While you said, "there is no tidy equation we can use to calculate any integral we want." While that's true, there is a tidy equation for the kinds of curves we are using in this course. Just explain that for the purposes of this course we're going to use simple formulas for modeling positions and velocities, and here are the ways we do derivitaves and integrals on them. Leave the explanation that integrals in general are tough for a crash course calculus.
As much as I love this series, it is incredibly ambitious. Physics is a very complicated subject. You have ten minutes. To dive right into calculus based physics and expect to convey any reasonable understanding is a pipe dream. Anyone who understood this video likely already knows the material. I suggest you guys give an overview and help develop an interest in and a curiosity about basic principles in physics rather than try and teach how to do the calculus in a 10 minute lecture. Peoples heads are going to explode.
Yeah calculus isn't something you can just shoehorn into 2 10 minute videos, crash course calculus would've been a good series to do before this one so people had an understanding going into this one.
Exactly. They're gonna loose part of their audience soon if they keep bombarding people with numbers. It's no use if the only ones who like the vids are the ones who already know it
Love the Feynman lectures in the back there
+Adam Smith Those are on loan from Henry of Minute Physics. :)
-Nick J.
Dr. Somara. You're surely short of time. After 15 years I picked it again. My fear of Physics and Maths reinstated. Thanks to YOU KNOW WHO...
I think the problem with these two episodes is that so much is presented by fiat... the Newton quotient made a brief appearance in the last video, but slowing down just enough to outline how you get from there to the power rule and the derivative of e^x would have worked wonders (plus, as I said in the comments of that video, giving a geometric argument for the derivative of the sine rather than the very very handwavy "argument" given), as well as a minute or two to go over the connection between antiderivatives and Riemann sums.
Its a physics course though not calculus. Khan academy does a great job of fully covering calculus
It's called "Crashcourse" for a reason
My maths B teacher took about 4 lessons to teach basic integration. She is relentlessly moving through this content. 😂😂
Hmm. Since this course is heavily math based maybe it would be useful to put out practice equations so people who are trying to seriously learn along can get a better grasp of the concepts.
+Samantha Stroiazzo I definitely agree. Having only one video on differential and integral calculus each is not nearly enough to be able to learn the subjects.
+Samantha Stroiazzo teaching calculus takes a ton of time, and that's just not the point of this series imo.
BUT, luckily, we're on the internet, and there's a place for everything.
here on youtube that would be khanacademy, with a playlist of 200! fantastic videos that'll get you through most of those two semesters of university calculus shini mentioned.
+DerUnbekannte Of course. Everyone should know about Khan Academy. BUT, what would be useful is having a few practice worksheets to help ground the ideas only presented here in clear reference to the scenarios given. Shini goes through them fast with the understanding that it will be important but not essential. This is not a course on Calculus but Physics. I just think that having maybe 5 example of the math based exactly on just the math represented would be helpful. A clear 1:1 instead of searching through 200+ videos trying to learn something covered in 1 10 minute video.
Samantha Stroiazzo sure, it wouldn't hurt
please keep this series up. As a mathematics major I find this very helpful. I knew how to find derivatives and integrals but I never knew what they were used for. now I can use this in my physics course!
+aaron mack Jesus... You didn't know what they were for? have you never done any flow rate problems? Volume of a curve rotated around an axis? electrical impulse problems? If you are even past your first calc class I find that hard to believe.
ArchesBro I have done those. But my professors never told us what the uses were for just how to do perform them I had to look up the uses myself.
+aaron mack Do you mean you do maths at school or university?
BlueCosmology I'm in college
BlueCosmology I was in ap classes in high school but even then then didn't teach you what we were learning just how to do everything.
I love these videos keep up the great work ! I wouldn't mind if she spoke not so quickly during parts that require us to think a little about what's been said. On a side note, a beautiful woman into physics, too good to be true.
What a beautifully made video!
Nooooooooooooooo!!!!!!!!!! When you start with "integral safe the inverse of derivatives" you rob the fundamental theorem of calculus of its beauty!!! *cries mathematically*
+gyinagal I get that they want to make it simple for the casual viewer to understand, but man, the weight that the fundamental theorm of calculus hold and the way professors hype it up in schools and they way they introduce it is so worth it lol
+gyinagal I learned integration only as the "inverse" operation of derivatives first, then we established the connection with curve area, found that more beautiful!
Wow, autocorrect. Integrals ARE*
I like the new show. I am guessing she is showing us calculus so we know where the equations come from. Hopefully she will proceed with algebraic equations and the calculus will make sense as we continue. Knowing a little calculus will be helpful in knowing which equation to choose. Learning the units can also be helpful when picking an equation.
Very useful! Don't let the non-physicists get you down. Keep up the good work!
+Harrison Wade Pretty wasteful to make a phys intro course if only physicists are going to understand, don't you think?
Not in the slightest, that's its target demographic
Harrison Wade It hasn't been so far. I haven't been watching crash course economy because I have an econ degree and I know it's intended for people new to it. It should be this way too. I can follow the video because I already know calculus, but those who don't are gonna get lost.
jmiquelmb I haven't done calculus yet I understand this video. Perhaps I'm just working harder at it than others.
Harrison Wade Then trust me when I say that this is not a good intro to calc. You'll see in a future that she's been missing a lot of stuff. You can't properly explain calculus in 20 min.
You know what I felt so interested in physics after I have found a fundamental way to study physics while I was watching your video. Thx lots
I don't care how many times I have to repeat this I'm going to learn this and master it
+tragoedia veritas you have to try out some questions and maybe do some simple tests to gauge your understandig of it
Yea I know. I've been trying to memorize the equations while listening to the demonstrations and crunching the numbers. I think all math becomes easier once it's written out in front of you
haha good for you! it took me almost a year to understand the basics of integral to get it right, even then i'm still struggling.
I enjoy this physics "class" so far because it's approaching physics from a way that is unique from most courses
Somehow, where i'm studying, they managed to squeeze both derivatives and integrals into one semester.
At 4:40 and 5:44, your claims about the constant of integration only apply to certain cases. Many position functions in physics include expressions beyond simple polynomials. Examples include Euler's number raised to a variable time exponent and periodic motion represented by trigonometric functions. Rather than generalize, I'd mention that the initial value is found by evaluating the expression where time equals zero and that it may differ from the constant of integration.
i have my first year calc exam next week THANK YOU SO MUCH FOR THIS!!!!
+Hardev Lad then it isnt an exam right?
+matthijs achtersekte -- he said _first year_ exam, not FIRST exam.
I started watching this series but have up. I wasnt in the right place.
But now, in the last few months I took it upon myself to understand a few things is a mathematical sense. I relearnt my grade 12 maths and learnt some new stuff so I could fathom orbital mechanics and aerodynamics. I can now comfortably calculate the dV for a phasing burn, or the lift and drag of an aircraft.
But there's still so much I want to know.
Then I remembered Shini with the kickass series on crash course that I gave up on because I got scared of integers.
I now get integers, but that was only Ep3.
Sorry I'm late. Time to binge and scribble.
I know calculus but I still was confused by watching this video. The pacing is just so off. She's like "lol integrals are the opposite of derivatives right" and then talks about constants for a solid two minutes. y u do this, CC Physics?
+Schindlabua Yeah she should have talked about that in the derivatives video, and just said the rule as, the derivative of a constant C is zero. Then the +C would have been obvious in this video and she wouldn't have had to explain it.
+Schindlabua I personally would have explained vectors first. And then explain calculus much later. Why? Because you can relate vectors to velocity, distance, acceleration etc. Basically vectors actually match up more with the current content that has been covered.
+Schindlabua No offence, but it sounds like you don't know calculus, or you didn't learn it properly.
+vdeave No way. This is no way to introduce calc to people new to the idea. Imagine your first calc class was these two videos being projected onto the screen. This series has been pretty bad so far, even if I don't like to recognise it.
jmiquelmb Oh yeah, I agree it's done a pretty bad job at introducing new people to calculus, but I'd think anyone who knew calculus already would follow it.
"And now you have everything there is to know Calculus... no you don't" died there of laughter. A painful and happy laughter. Please also tell us about Residue Theorem - a lot of physics use it... or don't tell us=)
If I cry hard enough I start to understand it...
This is better more understandable than my physhic high school teacher. He just gives us the equation. This explains more how the equation was created. Thanks for this course.
one year in college=20 min in crash course (#2 derivatives + #3 integrals)Value your time, guys!
So far, you've answered every question and cleared up most of the confusion I've had concerning physics. Thanks!
I mean I love this, but there are some things about this episode's structure that leave me a little unsatisfied. For example, if I were new to the concept of calculus, I'd have liked to be walked through the entire derivation and integration process a couple of times as seen on the same numbers throughout, whereas the last two episodes have only been showing separate individual steps of each, with different numbers at each step. This makes it harder to visualize, at least that's how I'd feel if I were new to this.
Moreover, this part ( 6:30 ) bothered me. Yes, I know this 9,81 is the Earth's gravitational acceleration, but someone who's completely new to this will be left wondering if they missed a step, because the number 9,81 seems to come out of nowhere for now.
Besides, you guys in the comments, remember that in some countries calculus is not taught at schools, or is only taught in a very small scope. For Americans it may be a review, but for many foreigners it's a whole new thing to get used to.
+corhydron111 Exactly. I think they should have covered vectors first instead of calculus.
Yeah, I mean I think it would make more sense to introduce the physical formulas first, just to give the students an idea of the possible applications for calculus, and then talk about the math behind all that.
+Geekminer
It's better to save vectors until you get to 2-D and 3-D motion. They would just be confusing (assuming you had never seen then before) when you are only dealing with 1-D motion.
+corhydron111
I disagree. You don't learn physics by memorizing formulas. You learn physics by understanding where the formulas come from, and to do that you need calculus.
Michael Sommers
I don't think Crash Course's videos should be used to learn material they're covering. It should be used as a reference or revision. Crash Course mainly caters to those who a reviewing a subject not learning it.
The graphic at 4:50 is misleading. The constant doesn't always equal the y-intercept, as the picture shows. This proposition is only certain for polynomials; a function such as e^x doesn't do this.
This seems more complicated than it needs to be. You genuinely don't care what value your speed is at any given time, what you need is the speed function. You also don't need to drag around C all the way back into the motion function. You can resolve it as soon as you find the speed function. A single constant is trivial to resolve as long as you know the function value for a specific value of the variable. We know the speed was 0 at time 0, so C is 0. Integrate the result again and you get the motion function with another constant. We know that the location was 0 at time 0, so you can weed that out, as well.
f(0) = 0
f'(0) = 0
f''(t) = 9.81
f(1.7) = ?
f'(t) = ∫f''(t)*dt = ∫9.81*dt = 9.81t + C
f'(0) = 0 9.81*0 + C = 0 C = 0 => f'(t) = 9.81t
f(t) = ∫f'(t)dt = ∫9.81t*dt = 1/2(9.81)t^2 + C = 4.905t^2 + C
f(0) = 0 4.905*0^2 + C = 0 C = 0 => f(t) = 4.905t^2
f(1.7) = 4.905*(1.7)^2 = 4.905*2.89 = 14.17545
Mind you, all of this is assuming our graph is upside-down. With cartesian coordinates, g would actually be -9.81, since it would accelerate items "down" while the y axis (which is what we're using here to determine "height") is positive in the "up" direction and negative in the "down" direction. Technically, the "height" of our window from the origin point of "us" would be -14.17545m, meaning the ball ended up ~14 meters below us.
I find it refreshing....makes you pay closer attention.
I consider myself a reasonably smart fellow, but this video, same as the previous one, reminded me that maths is the one thing I have real trouble understanding. At least at this pace.
I'm Alg 2 Honors as a freshman, can't wait for AP Calc in Junior year!
+Bryan Coronel Be worried. Be very worried. Calc isn't algebra. after several years of calc and algebra and actually using some of it (like maybe 10%) Calc and algebra are just two completely different beasts. If you do really well in algebra (like myself) you'll struggle in calc. If you do really well at Calc (like a very good friend of mine) you'll struggle at algebra. Don't know why it works like that but it just does. It's just a totally different way of looking at math. I switched everything up and said screw math, math and went statistics. which is still math, but we also have to interpret our findings. Always take a stat class if you can. calc is great. but I'd honestly suggest ap stat if you can take that instead. it'll be boring but once the easy stuff is out of the way then you can get into relevant data analysis and regression and that's what will set you apart from anyone else looking for jobs. You know and understand statistics.
In The Netherlands we already cover a bit of calculus in middel school, like limits, derivitaves and integrals
we are learnig this subject at highschool. my brain was in a liquid form when i finally understand it
I can appreciate the disclaimer at 9:10, but it seems that the fact that it wasn't explicitly asserted beforehand that one cannot learn calculus from two 10-min videos alone is causing grief for a lot of viewers. I've had previous exposure to calculus and can say that these videos really have strengthened my understanding of it. I also understand why the subject was only scratched and not left out of the physics course entirely. I just think that the audience needed a stronger reminder that if they really want to master calculus and physics, they'll have to treat these videos as introductory/supplementary material.
Then again, it is CRASH Course. Maybe people should know better.
+KVergara Unlike the history video series or economic series these videos are very difficult to follow and only apply to a very small audience. One that has been introduced to calculus but not gone too far in.