Which Book Offers Intuitive Insights for Advanced Mathematical Methods?

[Joker93]

Hello, i am currently enrolled in a Mathematics course which covers these subjects:
-Calculus of Variations
-Laplace Transform
-Fourier Analysis
-Special Functions
-Integral Equations
And as an introduction to the subject it has several things from calculus like maxima/minima of functions of several variables, some differential(also partial differential equations) equations, Jacobians, Lagrange multipliers, Leibniz rule and partial differential equations(primarily the variable separable method).

Could you please recommend to me a mathematics book(either an applied mathematics book(for mathematicians) or a mathematical physics book or a mathematical methods for physicists book) that covers these but offers intuition(and has graphs) rather than just emphasizing on calculations?

 

[jedishrfu]

Prof Nearing's free ebook covers some of these:

http://www.physics.miami.edu/~nearing/mathmethods/

others would be Arfken and Weber:

https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20

You can read Arfken book's table of contents at Amazon.

 

[UnivMathProdigy]

Books on this topic are piquing my interest as well, but most of the books I might recommend don't really cover integral equations, except for one of them.

• Mathematical Methods in the Physical Sciences by Mary L. Boas
• Mathematical Methods for Physics and Engineering: A Comprehensive Guide by K. F. Riley
• Advanced Engineering Mathematics by Michael D. Greenberg
• Advanced Engineering Mathematics by Erwin Keryszig
• Mathematical Methods in Physics and Engineering by John W. Dettman (this one has a chapter on integral equations)

Hope this helps.

 

[deskswirl]

Advanced Engineering Mathematics by Erwin Keryszig

<- is the most readable in my opinion although it isn't as high level as some of the others. Has nice relevant pictures also.

Linear Integral Equations by Lovitt (Dover reprint) is very intuitionist, although it doesn't have graphs (era 1920s), but very clear exposition covering Fredholm, Schmidt-Hilbert, and the Louiville-Neumann method.

The Fourier Series (older) book by Byerly is also very intuitionist and also covers PDE separation of variables (this also was a dover reprint at one time). For general Fourier Analysis I recommend the Schaum's Outline by Spiegel. Additionally his Laplace Transform and Complex Variables Schaum's Outlines are useful.

For calculus of variations look for van Brunt. This is a recent publication but you might check your university library.

For complex variables (I'm assuming this topic will be at least skirted although you didn't say) look for Carrier, Krook and Pearson. It is the best of the lot although the problems can be difficult. If you need the basics of complex numbers prior to that start with the first volume of Knopp called Elements of the Theory of Functions.

Stay away from Arfken as the organization is really lacking and he moves quickly over important details. Boas is okay but reads like a cookbook. Additionally Mathews and Walker has a lot of nice tricks but you might not learn much the first time around. Avoid Hassani's Mathematical Physics unless you have ALOT of time and like proofs.

...I'm guessing you are needing supplementary material so only suggested such types.

 

[George Jones]

Avoid Hassani's Mathematical Physics unless you have ALOT of time and like proofs.

Hassani also has written an undergraduate text, "Mathematical Methods for Students of Physics and Related Fields".;