Math tricks for Theoretical Physics

[Silviu]

Hello! Is there a book (any kind of written collection) about mathematical tricks for complex problems (in both math and theoretical physics). Over time I have encountered several nice and impressive tricks to simplify apparently difficult problems and I was wondering if someone gathered them in any way. To be clear I don't want a book with math applied to physics, at least not the kind of book that starts with "what is a vector".

 

[berkeman]

This is for fairly basic math tricks and shortcuts, but is a good place to start, IMO.

https://www.amazon.com/dp/0471575631/?tag=pfamazon01-20

 

[mpresic3]

I believe with experience, most physicists collect a grab bag of quick techniques and methods to solve or simplify problems so they can be done quickly. However, I believe pursuing a scattered collection without a body organizing these methods is misguided

I especially found that learning a few general powerful methods that can be applied to a wide variety of physics problems is worth a lot more than a collection of tricks.

I found that understanding the theory of quadratic forms can be applied to quantum mechanics, classical mechanics (both small oscillations, and rigid body problems), linear system theory, optimal control, electric and magnetic circuits.

The theory of special functions can be applied and is important to all these fields as well.

I once had a professor that solved many problems with "tricks". It was difficult to transfer his techniques to real-life problems which were unlike the assigned problems in textbooks which were contrived so that everything works out just right. I tried to present physics to my students to illustrate the method for solving problems, even if I could cleverly solve the problems with a tricky turn. Occasionally, I would show them the easy way, but I would discourage looking for easy ways for every problem. Sometimes physics problems are just hard