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

• Applied
• Bertin
In summary: Definitely check it out. That's another classic. It's full of gems about all kinds of "special functions". Definitely check it out.
Bertin
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.

Last edited:
yucheng and Delta2
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

yucheng, Bertin and Delta2
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!

Delta2 and vanhees71
Bertin and vanhees71
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.

Bertin and vanhees71
vanhees71, Bertin and hutchphd
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.

vanhees71
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...

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. vanhees71 and yucheng 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 wow I'll check out Churchill. Thanks!

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".

## 1. What is a bibliography?

A bibliography is a list of sources used in a research paper or project, typically at the end of the document. It includes all the information necessary for readers to locate and access the sources cited.

## 2. What is integration in physics?

Integration in physics is a mathematical process used to find the total or net value of a quantity over a given interval. It is commonly used to calculate the area under a curve, which has many applications in physics, such as calculating displacement, velocity, and acceleration.

## 3. What are ODEs and PDEs in physics?

ODEs (ordinary differential equations) and PDEs (partial differential equations) are mathematical equations used to model physical phenomena. ODEs involve a single independent variable, while PDEs involve multiple independent variables. They are used to describe relationships between variables and their rates of change in various physical systems.

## 4. What techniques are used to solve ODEs and PDEs in physics?

There are various techniques used to solve ODEs and PDEs in physics, including analytical methods, numerical methods, and computer simulations. Analytical methods involve finding exact solutions using mathematical techniques, while numerical methods use algorithms to approximate solutions. Computer simulations use computational methods to solve complex systems of equations.

## 5. Why is it important to have a bibliography on integration and ODE/PDE solving techniques for physics?

A bibliography provides a list of reliable sources for further reading and research on a specific topic. In the field of physics, where accuracy and precision are crucial, having a bibliography can help ensure that the information and techniques used in solving ODEs and PDEs are valid and reliable. It also allows for proper credit to be given to the original sources of information.

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