Math book recommendations for physics undergraduate

[Doplersleg]

Hi,

I have completed my first year of studies, a year that was rather hard. So I am in need of some good books(or book) to revise my hole year of math. Mostly I need to revise calculus and vector calculus, as well as differential equations. Basic linear algebra would be great too.

Although I do have some knowledge of my mentioned topics, I had some trouble with basic understanding of some of the concepts, so the books shouldn't be very "deep". An as I am studying physics, it would be great if those books would relate math concepts with physics.

Thanks

 

[Patrick_Nth]

Not so much a recommendation, but something you should probably avoid would be Arfken & Weber's Mathematical Methods. The Math Methods for Physics course I took last quarter required it, and it was terrible. Definitions throughout it are sparse and there is very little intuition behind any of it. I heard Mary L. Boas' Math Methods book was a much better alternative.

On the other hand, I've heard nothing but good things about the following:
Calculus - Michael Spivak
Ordinary Differential Equations - V.I. Arnol'd
Linear Algebra Done Right - Sheldon Axler
Intro to Linear Algebra - Gilbert Strang
Calculus Vol. 1 and 2 - Apostol

The first chapter of Griffith's Electrodynamics (3rd Ed. now) serves as a nice mini-review for vector calc as well.

 

[Dragonfall]

Linear Algebra Done Right - Sheldon Axler

Hey, I used the same book! I love that book.

 

[Doplersleg]

How's the Mathematical Methods for Physics and Engineering: A Comprehensive Guide
by K. F. Riley M. P. Hobson S. J. Bence ?

 

[Heresy]

Not so much a recommendation, but something you should probably avoid would be Arfken & Weber's Mathematical Methods. The Math Methods for Physics course I took last quarter required it, and it was terrible. Definitions throughout it are sparse and there is very little intuition behind any of it. I heard Mary L. Boas' Math Methods book was a much better alternative.

On the other hand, I've heard nothing but good things about the following:
Calculus - Michael Spivak
Ordinary Differential Equations - V.I. Arnol'd
Linear Algebra Done Right - Sheldon Axler
Intro to Linear Algebra - Gilbert Strang
Calculus Vol. 1 and 2 - Apostol

The first chapter of Griffith's Electrodynamics (3rd Ed. now) serves as a nice mini-review for vector calc as well.

OP said s/he doesn't want anything deep, so I don't think Spivak or Apostol is for him/her...

One of my friends in engineering loves Stewart's Calculus text, that's for sure.

 

[Patrick_Nth]

OP said s/he doesn't want anything deep, so I don't think Spivak or Apostol is for him/her...

One of my friends in engineering loves Stewart's Calculus text, that's for sure.

Whoops. Missed that part. I used Stewart's for my first round of vector calc and liked it.

 

[WiFO215]

Intro to Linear Algebra - Gilbert Strang

I'd tend to disagree. I'm not particularly fond of this book. Try Hoffman and Kunze. It's a little more rigorous.

 

[slider142]

Many students tend to miss a lot of the physical motivations behind divergence, gradient, curl and the Laplacian, all of which is expounded upon in the little book "div, grad, curl, and all that" by Schey. Completing the exercises in this short informal text will give you an innate sense of these common operators. A very useful text for a physics major.

 

[Patrick_Nth]

I'd tend to disagree. I'm not particularly fond of this book. Try Hoffman and Kunze. It's a little more rigorous.

I'm not too surprised. Probably the most scathing criticism I've heard about it was that it "teaches engineering math instead of real math". I myself have never used it although the Math Dept. here just switched to it from the LA book by Otto Bretscher (which I thought was terrible) for the lower-div sequence here.

 

[qspeechc]

I would not recommend Arnold for differential equations either, it's perhaps too advanced for one thing. Try Coddington's book.

 

[slider142]

I like "Ordinary Differential Equations" by Morris/Pollard myself. It is a nice survey of types of equations you may encounter and gives rigorous proofs and points out pitfalls appropriately. It is also very readable and very inexpensive (Dover publishing). Arnold you can save until you feel accomplished at techniques of solving differential equations and are curious about a unifying theory and the overarching geometric picture.