# Is it typical for some physics (math) to go over your head at first?

Long story short, I just finished Physics I. Since I'm currently attending a state college, I have been trying to study outside of my coursework in order to optimize my education and have the best chance of getting into top grad schools.

One of the resources I was trying to use was MIT's opencourseware Physics course from Walter Lewin. Now just to give you a bit of a background here, my math level is up to single-variable (I have multi-variable and ODE next semester). I also finished my Physics I course with a high A. However, while some of the material Lewin covers is easy for me, there are some things he does mathematically that go over my head. This is really frustrating to me since I have never struggled with anything previously.

Even with Calc II, I only spent 2hrs studying for our final and got a 100 on it. However, with Lewin's lectures, I feel like some of the mathematical derivations he uses is over my head. I remember a lot of the formulas at this point through the concepts and am not sure if I am falling short of being up to par with what MIT would expect? I recognize or can derive some of what Lewin does at times, but sometimes, I just can't follow him from point A to point B in his lectures.

I am planning to apply to places like MIT for grad school, so I want to make sure I'm not falling behind at this point. I have heard some professors will talk over your head since they will give you mathematics you may not have gotten to yet or such, but I am just not sure if he is one of those professors. I'm wondering if once I get through multi-var. calc and ODE if it will help the mathematical derivations make more sense, or if I should be utilizing some kind of resource to get better at that myself?

mfb
Mentor
I just can't follow him from point A to point B in his lectures.
Does it involve points where multivariate calculus or ODEs are used?

In general: yes, this can happen.

Student100
Gold Member
What are you having trouble with exactly?

You have to realize that what MIT put's out in the open courseware is only part of what students go through while attending classes. I've never watched the lectures, so I can't really comment on "if he's just talking over their heads."

WannabeNewton
Well for starters, it's MIT. Secondly, Lewin's 8.01 lectures don't go beyond single-variable calculus so if you're having trouble with his mathematical derivations then you might not have had a rigorous enough course sequence in single-variable calculus (although that's hard to believe since there isn't much mathematical rigor in the 8.01 lectures to start with). In the past, MIT had a more rigorous introductory mechanics course called 8.012 i.e. honors introductory mechanics, and it used Kleppner and Kolenkow (although if you look at past homeworks from 8.01 there are select problems similar to those and identical to those in Kleppner). This was the course name from a few years ago; I don't know what it's called nowadays.

Keep in mind that getting good grades in a class doesn't equate to having a deep understanding of the underlying subject material. It's not at all hard to get an A in a class without having a deep understanding at all of the subject matter depending on the university you attend and the target audience of the class taken (e.g. honors mechanics vs. regular mechanics).

You should identify exactly what it is that you are having trouble understanding in the 8.01 lectures in order to get useful recommendations as to how you can ameliorate your current situation.

Since some of the same questions were asked by all of you, I'm going to just respond with a general reply to some of it here.

As far as what I had a hard time grasping, one example is in lecture #11 at 8m30s on (http://ocw.mit.edu/courses/physics/...echanics-fall-1999/video-lectures/lecture-11/) related to the integration of work. We only briefly touched on 3-d vectors in our course, so what Lewin went over in that part threw me off. The only integrals involving work that we did with our course involved an equation for the force applied (quadratics, square roots, etc.) or a constant force applied for some distance. We also never changed directions with work applied, so I got lost on this.

Another part where he lost me was in lecture #20 from about 1m on (http://ocw.mit.edu/courses/physics/...echanics-fall-1999/video-lectures/lecture-20/). Although I understand and have worked with the angular momentum formula Iw, when he covered this, it completely threw me off. At about 15m38s, where he says "you see immediately... I hope that you see immediately," it made me want to punch myself in the face, because I had no idea how we were supposed to "see it."

Though I'm not sure of where a third thing I got stuck on was, I do remember it was something where he had some things like "dx" "dt" "dv" and things like that, moved them around an equation, integrated, substituted some of the "d" portions with their equivalents (ex.: a=dv/dt), kept some variables as constants and others were integrated as variables, and used it to derive a formula from some other formula. I have no idea where it was in the lectures, but the only time I ever saw something like that was when our calc II teacher briefly touched on the things you go over in ODE. So, not sure if we just skipped something we should have covered, or if it is something that will make more sense after ODE.

As far as a deep understanding, our course focused far more on problem solving than what I have seen in Lewin's course. Our problems were actually harder than the ones I tried on their first 3 exams, but we didn't delve much into derivations. A lot of times, it was just "here's the formula for work-energy," or "here is the formula for momentum-impulse" without many of the derivation explanations Lewin gives on them. Rather than focusing on the derivations, we looked at tons of problems where we had to figure out how to apply the formulas we learned.

I guess if I had to sum up what throws me off generally speaking, it is when he starts getting into various vectors on diagrams along with integrations involving multiple "d" components (dL, dr, dt, etc.), swapping around variables for other variables, etc. The concepts behind everything are easy for me, and when I read the material from the book for their course and ours, it's easy. However, when he shows how to take a formula and turn it into another using steps like I mentioned, it sometimes takes me quite a while to grasp it, where I have to read and re-read my notes on it and toy with it myself to actually understand it.

WannabeNewton
I guess if I had to sum up what throws me off generally speaking, it is when he starts getting into various vectors on diagrams along with integrations involving multiple "d" components (dL, dr, dt, etc.), swapping around variables for other variables, etc.
Ahh ok, I see now. Perfect

Well if it makes you feel better, I can't recall seeing or using these techniques in my high school calculus course either in any way shape or form, but I did use them extensively in my high school physics course.

However I would say that the place I really got practice with techniques such as drawing diagrams in order to deduce equations involving differentials of various physical quantities, manipulating these differentials in order to eventually get a desired result by means of integration etc. is from doing the problems in Kleppner and Kolenkow "An Introduction to Mechanics". Kleppner is basically a gold mine of problems that will make you adept at using said techniques. One problem that immediately comes to mind was from the chapter on energy and involved finding the average force on two walls wherein a ball is bouncing back and forth between the walls and one wall is slowly brought closer and closer to the other continuously (this problem also gives you practice with the use of binomial approximations in physics problems).

So you shouldn't feel bad if you haven't gotten any practice with techniques of the above nature in your calculus classes. If you can get your hand on a proper mechanics text that has problems aimed at giving you thorough practice with the above then just work through it and you should be fine

Ahh ok, I see now. Perfect

Well if it makes you feel better, I can't recall seeing or using these techniques in my high school calculus course either in any way shape or form, but I did use them extensively in my high school physics course.

However I would say that the place I really got practice with techniques such as drawing diagrams in order to deduce equations involving differentials of various physical quantities, manipulating these differentials in order to eventually get a desired result by means of integration etc. is from doing the problems in Kleppner and Kolenkow "An Introduction to Mechanics". Kleppner is basically a gold mine of problems that will make you adept at using said techniques. One problem that immediately comes to mind was from the chapter on energy and involved finding the average force on two walls wherein a ball is bouncing back and forth between the walls and one wall is slowly brought closer and closer to the other continuously (this problem also gives you practice with the use of binomial approximations in physics problems).

So you shouldn't feel bad if you haven't gotten any practice with techniques of the above nature in your calculus classes. If you can get your hand on a proper mechanics text that has problems aimed at giving you thorough practice with the above then just work through it and you should be fine
Thanks so much for the feedback. I actually bought the Intro. to Classical Mechanics book by Morin a while back, but I haven't gotten to it yet. Do you think Morin would be good to work on in place of Kleppner or does it not cover some of what you were thinking of in the Kleppner book? Also, do you think I would be better off continuing to browse the Lewin course or just work on the Morin book instead? There's so much to study and learn from that I have a hard time making up my mind what to put my time into?

WannabeNewton
Oh yeah Morin is also an amazing resource for problems that will hone your skills in using the above techniques as well as other techniques; it has some incredibly conceptually difficult problems that should have you pacing back and forth for a good amount of time.

If time is an issue then just stick to Morin; if you have time then use both Morin and the Lewin lectures in conjunction. However I must warn you that Morin is basically a problem book, it isn't pedagogical.

Oh yeah Morin is also an amazing resource for problems that will hone your skills in using the above techniques as well as other techniques; it has some incredibly conceptually difficult problems that should have you pacing back and forth for a good amount of time.

If time is an issue then just stick to Morin; if you have time then use both Morin and the Lewin lectures in conjunction. However I must warn you that Morin is basically a problem book, it isn't pedagogical.
Thanks again for the information. It has been extremely informative. I think I will split up my physics studies over the break between Lewin and Morin equally then.

jasonRF
Gold Member
... and toy with it myself to actually understand it.
This is the way real learning works, in my experience. I recall feeling the same way in my intro physics courses at times. It was only by toying with things on my own that I really learned them. The students at MIT have probably seen much of this material before; those that haven't may be brilliant enough to "get it" the first time through in lecture, but most people, even most MIT grads (I work with a bunch of them) have to work through things for themselves to really learn them. There is no substitute for this.

Also, I would say that it was in physics that I really learned how to use calculus. First semester physics was great, but there were a few things I did not understand so well. Second semester really drilled some important basic concepts into me. For example, an integral is just a sum of a bunch of very small things. That is the best way to think of integrals, not as "areas under curves" or other such things that fall into the more general "sum of a bunch of very small things" category. That is what Lewin did lecture 11: $dW = F_x\, dx + F_y\, dy + F_z\, dz$ is simply a very small thing. A bunch of these very small things are then added up via the integral.

Keeping working and thinking - I think you are on the right track.

Jason

Student100
Gold Member
Thanks again for the information. It has been extremely informative. I think I will split up my physics studies over the break between Lewin and Morin equally then.
So out of curiosity, I've been watching some of the lectures tonight.... Are you following the modules they have set up or looking at the indexed course? The way the modules are set up they seem to skip around a bit.

This is the way real learning works, in my experience. I recall feeling the same way in my intro physics courses at times. It was only by toying with things on my own that I really learned them. The students at MIT have probably seen much of this material before; those that haven't may be brilliant enough to "get it" the first time through in lecture, but most people, even most MIT grads (I work with a bunch of them) have to work through things for themselves to really learn them. There is no substitute for this.

Also, I would say that it was in physics that I really learned how to use calculus. First semester physics was great, but there were a few things I did not understand so well. Second semester really drilled some important basic concepts into me. For example, an integral is just a sum of a bunch of very small things. That is the best way to think of integrals, not as "areas under curves" or other such things that fall into the more general "sum of a bunch of very small things" category. That is what Lewin did lecture 11: $dW = F_x\, dx + F_y\, dy + F_z\, dz$ is simply a very small thing. A bunch of these very small things are then added up via the integral.

Keeping working and thinking - I think you are on the right track.

Jason
Well thanks for the feedback.

I had some more time tonight to really look over more of his lectures. I think a part of my problem was skipping the easy stuff he covered and jumping right to the stuff that was new to me without knowing his method of instruction. Once I went back to some material I knew well and watched how he taught it, it started to click with me. I'm not going to say I grasp all of what I re-hashed on of his, but I definitely got the majority of it this time around.

So out of curiosity, I've been watching some of the lectures tonight.... Are you following the modules they have set up or looking at the indexed course? The way the modules are set up they seem to skip around a bit.
Well lately I've just been going through the video lectures and skipping through to material that is new to me, though I do feel that the order he goes in is a bit disorderly at times. In our course, we started in 1-D and covered kinematics, dynamics, and conservation laws. Then, we did the same for 2-D. Then, we added integration of functions into our force, impulse, etc. Each thing built on the previous concepts we learned.

I spent some time going through their book, but I stopped doing that about four weeks ago at chapter 8 when I just didn't have time to keep up with it. Oh, and I did some of the assignments and the first two exams.