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Currently I'm doing Advanced Classicial Mechanics courses.I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters.

Can anyone suggest a mathematical book which is dedicated to teaching all the math that is used in physics?

Thank you, Sai

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For calculus I would suggest . This bookd by anton biven davis makes calculus interesting – Harish Kayarohanam Aug 12 '13 at 19:53
What about V.I.Arnold's Mathematical Methods of Classical Mechanics, GTM60? – Frank Science Aug 13 '13 at 1:10
Why not get dedicated books for each topics and go through them? I heard good things about this book:… but it is probably more of an introductory book. It covers a lot of important topics though. – please delete me Aug 13 '13 at 5:16
The book from Arnol'd is like the books from Landau or Knuth: very nice, if you know that stuff already to a fair degree but I think not really suited to learning it the first time. – mvw Jun 6 '14 at 10:50
up vote 3 down vote accepted

Try Mathematical Methods in the Physical Sciences by Mary Boas. It's pretty comprehensive and easy to follow.

Also, Classical Mechanics by Taylor has a pretty decent section on inertia tensors (I'm guessing this is the linear algebra you need).

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I was planning to mention Arnold's book, which was mentioned by @Frank Science. This is a wonderful book but requires a little mathematical maturity to follow. I am trying to write this as a reply of the last line of your question.

Can anyone suggest a mathematical book which is dedicated to teaching all the math that is used in physics?

It is impossible to know every aspect of maths which has some use in physics. Moreover, mathematics books are generally written in a certain way which someone from a physics background may find strange. (Converse is also true. Mathematics students find lack of mathematical rigor in Physics texts as very disturbing.) It is better to know and understand the mathematical aspects used in the 'area which you are studying'. This will give you mare insight about the physical problems.

For your current problems with linear algebra, I suggest you look at Hoffman & Kunze. You can also see the algebra of Artin. I found this book very lucid and written in a way which is easy to apply for practical problems. A book of similar nature is Rudin, which you must read for analysis.

After reading Rudin (& gaining some more mathematical and physical understanding) you can try Methods of Modern Mathematical Physics by Michael Reed and Barry Simon (four volumes). This book does not cover all mathematical aspects a physicist may require, but it definitely contain a large section of useful ones. I like the end notes of each chapter where the background physical motivations are explained. These are not very easy books.

The only missing areas are (differential) geometry. I guess somebody else can tell about this better than me. I generally look at Nash and Sen.

All the best for your work.

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It might be a bit over your head now, but when you feel ready to take the next step, I have heard that Advanced Mathematical Methods for Scientists and Engineers by Carl Bender and Steve Orszag is a very nice book.

As a side note, his lecture series on Mathematical Physics is available on Youtube.

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There are 2 books that I used to help me, and what I use to help my students, maybe these will be of assistance to you:

This first one takes an interesting approach, it looks at Physics as learning a 'second language', in the book "Introductory Physics with Calculus as a Second Language: Mastering Problem-Solving" (Barrett, 2006). The emphasis on problem solving in this book makes it especially helpful.

The next example is a bit odd, but strangely has worked rather well, "Tha Cartoon Guide to Physics" (Gonick) - this book, despite its name, teaches Physics, with quite a bit of the mathematics in context (some of it somewhat sarcastic).

Also, the online tutorials from Khan Academy are very useful.

I hope this helps.

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I like learning by solving problems and I would recommend the Schaum's outline series, especially the books on

  • vector analysis,
  • mechanics,
  • complex variables and
  • linear algebra

also very helpful were the books on ordinary and partial differential equations and the book on tensor calculus.

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For a course in Advanced Classical Mechanics, my suggestion is to cover the background necessary as quickly as possible to understand the course.

In addition to the books cited in linear algebra,... knowledge in differential geometry is essential, my professor A. Mikhailov, uses these notes (can help you).

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Stroud Advanced Engineering Mathematics. Since you are struggling with some basic Calc 3 (multivar) and Calc 4 (DiffyQ) stuff, you need a book that is there to teach you, not to make things hard. Schaum's Outline would be another good one. Review Calc 3 and DiffyQ within there. You can also use them for harder topics later (Bessel function fun).

BTW, it seems like a lot of the math methods books (Boas, Kreyszig) have a tendancy to review multi-var calc and ODEs as well as covering "advanced" topics. [Which is strange to me as many schools have dedicated classes with dedicated texts for Calc3 and ODE and it makes those books fatter. But this is an aside.] Since you have had those classes before, think these books will be fine for you. I personally found Kreyszig very easy and painless for ODE review (but never worked through the rest of it and some people complain about other parts of that book.)

Avoid Arfken/Weber except if you want to buy it to just look fancy or as a reference for later. Since you are struggling with basic material, you need easier books. Probably Stroud > Schaum's > Boas > Kreysig > Arfken in terms of easiness and friendliness to a learner who is struggling.

Definitely avoid Rudin. You need some help with the basics, not a "done right" rigorous treatment.

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