Self-studying post-calculus level?

College Majors Engineering Majors
1

<p>Hey, I'm looking for honest advice from college students who went through rigorous classes in physics/math.</p>

<p>As a prospective 2nd semester senior, i'll have a lot of free time: time for math, time for science competitions, but most importantly, time to delve into some topics of interests (Stoke's theorem etc...). I am planning to major in physics or engineering, and would like to have a very strong base in math/physics before I come to college, so I can have an easier time 1st semester. </p>

<p>Here is my background:
-AP calculus BC (now enrolling)
- Physics C (now enrolling)
- Physics B
- Chemistry AP
- some science/math olympiad experience. A pretty weak problem solving skill set though (6 on AIME). :(</p>

<p>With AP credits, I'll probably have the following math/science classes 1st year (quarter system)</p>

<p>-Multivariate calculus/ODE/Linear algebra
-Mechanics/E&M/Modern physics (for physics major series)
- Maybe, i'll double up with Organic Chemistry, if I'm allowed to.
- some humanities classes+ intro engineering (If I major in engineering)</p>

<p>To prepare for that rigorous schedule, what can I do ahead?<br>
What made your 1st year hard, especially if you skipped using some AP credits?
What would you have done different to prepare for those tough classes, had you been a high school senior?</p>

<p>I have a multivariate calculus book (I'm already midway through), a differential equation textbook (just started), a linear algebra book, Fourier Analysis book, and Halliday Resnick physics book. I can buy cheap used books, and I find the Introduction to Mechanics by Kleppner and Kolenkow quite irresistible. I'll also use MIT ocw and youtube quantum mechanics lectures (for fun :)) Keep in mind I want to ace those intro classes.</p>

<p>Thanks for the help.</p>

2

<p>I'm a Stanford engineering freshman. From your previous posts I assume you got into MIT or some place similar? Lol I got 7 on AIME, so we're in the same boat :)</p>

<p>Study linear algebra along with multivariable calc or diff eq; it makes concepts in the latter courses more elegant and generalized. For example, vector-valued functions can be viewed as a mapping from R to R^3. Systems of ODE's can be solved using matrix methods.</p>

<p>One of the mistakes I made was take "math for engineers," which emphasized computation and skimmed on proofs. It's appropriate for others, but apparently not you. I don't know if your school makes the distinction.</p>

<p>Yeah... MIT OCW is great! Definitely go through the physics series; they're so much more rigorous than AP. College classes go very fast so don't go beyond 4 big classes your first semester; also class shop first. BTW send me your gmail or aim if you want. Good luck.</p>

3

<p>Also, review your calculus rigorously, like looking at the proof of the fundamental theorems of calculus. It helps a lot!</p>

4

<p>Haha... how ironic, I actually got into Stanford. Hey buddy, we might be partners next yr!! Yay!</p>

5

<p>One thing I found that kept surfacing in engineering classes, and upper level math classes was techniques of integration (parts, u-sub etc). A lot of people forget them, and they have a way of landing up on tests. </p>

<p>Also, trig identities find their way into all sorts of problems. They are easy, but a lot of people (myself included) suffer from over confidence, and end up messing up on stupid problems.</p>

<p>Other than that, you should be fine. If you like to study by yourself, you could probably do research in your Junior/Senior year, perhaps through the schools honors college. Then your efforts will be more productive because you will have had more classes, and so be able to solve more complex problems.</p>

6

<p>6 on AIME is bad?!?!?!</p>

<p>hell, that might be poor for you, but there's a whole bunch of us regular guys who still can't make that illustrious 100+ on the AMC!</p>

<p>a 6 is fine - in any reasonably high ranking university that would still put you in the upper tier of mathematical ability (except for a university like MIT).</p>

7

<p>"If you like to study by yourself, you could probably do research in your Junior/Senior year, perhaps through the schools honors college. Then your efforts will be more productive because you will have had more classes, and so be able to solve more complex problems."</p>

<p>Well, I'm actually a senior right now geared w/ a lot of AP courses. However, I truly want to ace my first year classes. I already did some biochem research, but the material that I learnt was way beyond anything I'll do 1st yr, and way specific for me to fall upon in my 1st year.</p>

<p>"6 on AIME is bad?!?!?!</p>

<p>hell, that might be poor for you, but there's a whole bunch of us regular guys who still can't make that illustrious 100+ on the AMC!"</p>

<p>Haha, I guess I spend too much time on AoPS :) And BTW, I didn't even make 100 on my AMC12, I made a 99 and qualified (OK, I didn't study at all for my AMC)</p>

8

<p>I was thinking about doing the same thing during the winter break. I like my Calculus by James Stewart textbook for self study and Calculus by Howard Anton (which I'm probably going to buy later. My brother's taking BC Calculus too, so he's using that along with like three other books that's I'm taking advantage of xD). I use The Calculus Lifesaver by Adrian Banner for explanations and as well as videos by PatrickJMT on Youtube. </p>

<p>For physics, I'm going to use Feynman's lectures on physics and I kind of like The Mechanical Universe videos online. </p>

<p>Good luck! We should study calculus together lol. I'm taking Cal II and Physics I in the Spring xD</p>

9

<p>Invest time in learning Laplace transforms (Diff Eq). Extremely useful :)</p>

10

<p>How about you stop studying and just enjoy life? You sound like you have the brains to make it through most college level classes, so it might be a good idea to cruise through your last semester of high school and just enjoy life. If you start in college with classes like O-chem, Calc 3 and E&M things aren't going to be so fun all the time, no matter what you do (at least from my experience). </p>

<p>I guess if you really want to get ahead though, look into Stokes/Greens/Divergence theorems and how they work with things like flux/circulation/curl/flow etc. You probably won't use them until the end of the semester, but they actually are really cool (I can't believe I just called something in Calculus cool...) and useful. Also, having an understanding of all the components in the TNB frame and how they are related to each other could be a lifesaver for you on exams. The best thing to do is to work on your study skills, if you can master those you can master anything in college.</p>