The interaction between mathematics and physics need not be emphasized. What needs to be emphasized is that mathematics is not merely a tool that facilitates the presentation of physics, but is the only medium through which physics can survive.

Just as language is a means of expressing human thought, without which it loses its unique identity, mathematics is the only language in which physics can express it self, without which it loses its identity. And just as language is perfected through its constant use, mathematics undergoes its most dramatic development through its use in physics.

Some of the most beautiful mathematics has been motivated by physics (differential equations in Newtonian mechanics, differential geometry in general relativity, operator theory in quantum mechanics), and some of the most fundamental physics has been expressed in the most beautiful poetry of mathematics (dynamics in symplectic geometry, Lie group theory (fundamental forces in).

**About the Book**

This book is for physics students who are interested in the mathematics they use. It is also a book for mathematics students who want to see some of the abstract ideas they are familiar with come alive in applied situations.

Its level is that of an advanced undergraduate or beginning graduate student course (or series of courses) traditionally called” Mathematical Methods of Physics “or a variant there of. Unlike most existing mathematical physics books for the same audience, which are lexicographical collections of facts about matrix diagonalization, tensor analysis, LeJandre polynomials, contour integrals, etc., with little emphasis on the formal and systematic development of the topic, this book is a collection of formalism and application, abstract and It attempts to strike a balance between the concrete and the concrete.

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