Applied Bibliography on integration and ODE/PDE solving techniques for physics

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The discussion focuses on recommendations for integration and ODE/PDE solving techniques relevant to physics, particularly for someone transitioning into theoretical physics. The original poster expresses a desire to understand the mathematical foundations behind functions like the Riemann zeta and Legendre polynomials, emphasizing the importance of reducing complex problems to well-established solutions. Several classic texts are mentioned, including Courant and Hilbert's "Methods of Mathematical Physics," Morse and Feshbach's "Methods of Theoretical Physics," and Sommerfeld's lectures. Participants suggest additional resources like Abramowitz and Stegun for reference, and Whittaker & Watson for advanced topics, while also noting the value of easier introductory texts such as Churchill's "Complex Variables." The conversation highlights the necessity of a solid mathematical background to tackle these subjects effectively, alongside practical recommendations for further reading and exploration of mathematical techniques.
Bertin
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Hi, you all,

I open this thread to ask for any recommendation concerning integration as well as ODE/PDE solving techniques for physics. I love mathematics, and I usually read material on pure mathematics (most notably abstract algebra and a bit of topology) but here I'm more interested in the learning and practicing methods to solve ODEs, PDEs and general integrals, or at the very least, being able to reduce them to known equations whose numerical solution is well established (Hermite polynomials, Bessel functions, etc.).

I'm finishing my third year in physics with the intention of going towards theoretical physics, and even though I know basically everyone solves these problems numerically, I would like to dig in the equations and integrals that led to functions like Riemann zeta, the Legendre polynomials, the Airy functions, etc. I'm not as interested in learning their story as to practice how to reduce problems to these "solved" problems, since my purpose is to understand where these constants that appear in many equations of physics come from. Any recommendation will be appreciated. Oh, and by the way: I understand that it might be the case that integration techniques and ODE/PDE solving techniques might be treated in separate books.
 
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Classics are:

Courant and Hilbert, Methods of mathematical Physics (2 vols.)
Morse and Feshbach, Methods of Theoretical Physics
Sommerfeld, Lectures on Theoretical Physics, vol. 6
 
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vanhees71 said:
Classics are:

Courant and Hilbert, Methods of mathematical Physics (2 vols.)
Morse and Feshbach, Methods of Theoretical Physics
Sommerfeld, Lectures on Theoretical Physics, vol. 6
Ok, I see this summer I'll be eating Morse and Feshbach's chapter 4 and 5 for breakfast, the book seems delicious (and infinite). I'm very happy you recommended it, I was pretty frustrated by Arfken, Weber and Harris (although I understand that any book that size would find similar limitations). Thank you!
 
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Maybe get a few books in applied mathematics on these subjects?

If looking through it from a pure math perspective, you would need a lot of machinery before you can start.

For a decent intro pde (applied).

https://www.amazon.com/dp/1571460365/?tag=pfamazon01-20

Then look up articles on the topics you are interested in.
 
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MidgetDwarf said:
Maybe get a few books in applied mathematics on these subjects?

If looking through it from a pure math perspective, you would need a lot of machinery before you can start.
How about Whittaker & Watson? I like the sections on basic mathematical analysis.
 
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yucheng said:
How about Whittaker & Watson? I like the sections on basic mathematical analysis.
Im not familiar with this book. I read the table of contents, and some reviews on Amazon. Looks like a book on real analysis, that ends with analysis on the complex plane?
 
MidgetDwarf said:
Im not familiar with this book. I read the table of contents, and some reviews on Amazon. Looks like a book on real analysis, that ends with analysis on the complex plane?
It does discuss many differential equations and complex functions... but it's rather advanced for me...
 
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yucheng said:
It does discuss many differential equations and complex functions... but it's rather advanced for me...
I found a copy for $10 dollars, seems interesting. If you want an easier source for complex functions, Churchill: Complex Variables, may be of use.
Sometimes, it takes reading an easier book , in order to continue a current book.
 
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MidgetDwarf said:
I found a copy for $10 dollars, seems interesting. If you want an easier source for complex functions, Churchill: Complex Variables, may be of use.

Sometimes, it takes reading an easier book , in order to continue a current book.
10 dollars :biggrin: wow I'll check out Churchill. Thanks!
 
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yucheng said:
How about Whittaker & Watson? I like the sections on basic mathematical analysis.
That's another classic. It's full of gems about all kinds of "special functions".
 

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