Recommendations for Self-Study in Math and Physics for Engineering Students

[tamtam402]

First of all, sorry for my bad english, it isn't my primary language. I'll try to describe the courses I have taken as best as I can, since the school system and courses names here might not be the same as everywhere else.

I completed college-level Physics I, II and III courses. Physics 1 was on classical mechanics, Physics 2 was an introduction to E&M and Physics 3 was on optics, with some modern physics thrown in (basic stuff with spatial relativity, etc.).

I also have taken college-level Calculus I (derivatives), II (integrals) and III (double and triple integrals, more in-depth stuff involving the previous 2 calculus courses, etc.).

I also have taken a college-level linear algebra course, and a statistics course.


Here's my situation: I'm entering university as an Electrical Engineer, but I want to pursue my math and physics education. I know I'll see some advanced math and physics principes in EE, BUT it will be taught on a "do this to solve this" level. We might have a course on Fourier analysis (I don't know this stuff btw, all I know is that it's involved in signals) and be told to use formula Z to solve W thing involving signals. I have trouble saying this stuff in english, but what I'm trying to say is that as an EE at my university, we won't be teached the "basic" parts of the maths we'll use as good as I'd like.

I would like some suggestions on books to continue my math education, independently of my EE education. I will be in a co-op program and I'd like to go through maybe 1 book per 16 weeks internships (I'll have 5 internships in total). Here are my criterias though:

1) I'm not going to rush this. I'd rather take the time to learn everything I can from a book than half-*** learn 4 books.

2) I want to learn the next "logical step" in math. I know at this point I can probably learn a few different branches of math, but I don't even know what I can or can't learn (I don't know what's required to study X branch of math, what I should already know, etc.). At this point, I feel like I want to learn EVERYTHING. So recommend me books in a few different branches of math. If after these books I find myself interested by a specific branch, then I'll start reading about that field. However, everything interests me at the moment.

3) I'd like to learn how to write proofs on a math-undergrad level, if possible. Is this the kind of stuff that can be learned by myself? Is there any book in this? The "proofs" we've done so far are very basic, ex: proving the formula to solve a 2X2 determinent.

4) I feel like I learn better when I do exercices, so I'd like books with exercices if possible. Also, books that have at least the answers to the problems would be good, since I'll have no-one to turn to.

As a reference, Here are the first courses given to math students at a local university:

Discrete Maths (I know nothing about this)
Introduction to mathematical analysis (I think this is a "proof" course like I was talking about)
Algebra
Linear algebra (I guess this is a more advanced course on linear algebra since anyone in the math major will have taken the same college linear algebra course I had to take)

Thanks in advance if you can guide me. I'm very serious about teaching myself mathematics, and I'm a very good student. I hesitated between EE and math for the longest time, but I decided to apply for the EE university program. I figured I could teach myself the math I won't get to see, but I would've had a much harder time doing it the other way around (teaching myself EE).

 

[Daverz]

You probably have enough math and physics background to handle any "upper division" undergraduate physics books, e.g. Griffith's popular Quantum Mechanics text.

For a physicists perspective on "electromagnetics" -- which will surely be one of the central subjects of any EE degree -- I highly recommend Schwartz's Principles of Electrodynamcis.

I'd suggest The Feynman Lectures for general physics, though there are no exercises included.

For math, one book I find particularly fascinating is Visual Complex Analysis by Needham.

You should be able to find plenty of other recommendations by browsing around this subarea of the forum.