Calculus Checklist for Upper Division Physics Major

[TDRR]

Returning Physics Major (hopeful) needing a Calculus "checklist" for Upper Division.

Hello everyone, currently I've been out of school for roughly two years now. As the title suggest I'm a Physics major going into my first year of upper division. The first ourse is a "Intro to Math Methods in Physics" centered around the Mary Boas book ZapperZ has recommended. I'll be attending California State University, Fullerton and their Math prerequisite is simply Calculus III (Multivariable Calculus). There is no class dedicated to Linear Algebra or Differential Equations entirely as a Physics Major, they just go right into the Boas book.

I won't be able to start school for another year, which means I'll have plenty of time to review and perhaps learn Linear Algebra+Differential Equations on my own fom this book: *
https://www.amazon.com/gp/product/0130457949/?tag=pfamazon01-20
The book we used for the Calculus series at the Junior College I attended was James Stewart's "Calculus" which I'll be using again for review.*

For my Bachelor's degree, what parts of Calculus I-III should I absolutely must have down for what I have listed below. What do you feel I should place less emphasis on? It's tricky because I know where I stand for each section, but I don't know the importance of each section to a Physics major only going for their Bachelor's.



Calculus II:
Volumes of revolution-
Integration techniques- no problem with "by parts," trig inverses/trig subs/partial fractions/etc. Going to review improper integrals again, but it looks real easy. Every now and then I might run into a tricky integral where maybe I'll forget to use something like "change of variables" to make x equal to functions of u (not just a simple u-sub). Other than that though, I can do plenty of these in my head.
Conics- forgot all of that directrix/eccentricity/focus/major and minor arc stuff.
Polar coordinates/integration- going to review again, but also didn't have too much problems when using them in Calculus III.
Series- yikes. I have completely forgot how to do these. Will have to review everything.

Calculus III:
Surfaces in space: have to go back and memorize the formulas for ellipsoids/hyperboloids of one and two sheets/elliptic paraboloids/etc. I have completely forgot them all. Will these come up often?
Tangent planes and normal lines: need to review
Lagrange multipliers- had the concept down, but couldn't solve a few of the systems of equations.
Jacobian- ugh. I did poorly on this in school, and don't remember what this is about, at all.
Vector analysis (div, grad curl, vector fields, line integrals, Green's theorem, etc.): don't remember how to do these, had an easy time with them until surface integrals. The funny thing is after my Calculus-based E&M course I understood them much more, and even earned the highest grade in that Physics course. Of course the surfaces were only cylinders and spheres though, the surfaces in Calculus III were much harder for me, although I do understand the physical concept much better today.

I was able to achieve all A's in all of the Calculus and Calculus-based Physics courses while attending. But as mentioned, it's been awhile. As of right now, I'm just interested in doing well in the Thermodynamics, Advanced Mechanics (I believe the Marion text), Intro to Quantum And Modern Physics (I think the Griffiths text), and Advanced Electeomagnetics (Griffiths text most likely) courses- which I know means having the Math down pat.

Once again, any help would be greatly appreciated!

 

[TonyG]

Dear returning Physics major,

First of all, congratulations on your decision to continue your education in Physics! It's great that you are taking the time to review and brush up on your math skills before starting your upper division courses.

Based on the information provided, here is a checklist of the math topics that are important for a Physics major to have a strong understanding of:

1. Calculus I: It is important to have a good understanding of fundamental concepts such as limits, derivatives, and integrals. These concepts will be used extensively in your upper division Physics courses.

2. Calculus II: Volumes of revolution, integration techniques, and conics are all important concepts to have a good grasp on. Make sure to review these topics and practice solving problems. Improper integrals may also come up in your upper division courses, so it's important to have a solid understanding of them.

3. Calculus III: As a Physics major, you will use surfaces in space and tangent planes and normal lines frequently. Make sure to review the formulas and practice solving problems. Lagrange multipliers and Jacobian may also come up, so it's important to have a good understanding of these concepts as well.

4. Vector Analysis: This includes concepts such as divergence, gradient, curl, and line integrals. These are important for understanding vector fields and are also used in many upper division Physics courses. Make sure to review and practice solving problems.

5. Differential Equations: Although you mentioned that there is no dedicated course for this, it is still important to have a basic understanding of differential equations. They are used in many areas of Physics, including Thermodynamics and Quantum Mechanics.

It's great that you are planning to review and learn Linear Algebra and Differential Equations on your own. These are important topics for a Physics major and will definitely be useful in your upper division courses.

In addition to reviewing these topics, it's also important to have a strong foundation in algebra and trigonometry. These concepts are used extensively in Physics and having a good understanding of them will make your upper division courses much easier.

Overall, it's important to have a solid understanding of all the topics listed above. However, if you feel like you need to prioritize, focus on Calculus I and II first, as these are the building blocks for the rest of your math courses. And don't forget to practice, practice, practice! Solving problems is the best way to solidify your understanding of these concepts