Introduction to Mathematical Physics

This book is intended to be a survey of mathematical methods which should be available to graduate students in physics and related areas in science and engineering at an early stage in their careers. It may also be useful for practicing professionals who need an elementary introduction to the mathem [...]
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This book is intended to be a survey of mathematical methods which should be available to graduate students in physics and related areas in science and engineering at an early stage in their careers. It may also be useful for practicing professionals who need an elementary introduction to the mathematical areas covered in the text. In addition to the usual topics of analysis such as infinite series, functions of a complex variable, differential and partial differential equations, there is an extensive early introduction to the methods of differential geometry with examples chosen from classical mechanics, thermodynamics and electromagnetic theory. Some simple examples of nonlinear partial differential equations are discussed briefly. There is also a more extensive treatment of group theory than is available in current general mathematical physics textbooks. 1. Infinite Sequences and Series.
2. Finite-Dimensional Vector Spaces.
3. Geometry in Physics.
4. Functions of a Complex Variable.
5. Differential Equations.
6. Hilbert Spaces.
7. Linear Operators on Hilbert Space.
8. Partial Differential Equations.
9. Discrete Groups.
10. Lie Groups and Lie Algebras.