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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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 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.
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).