Mathematics for Physics: A Guided Tour for Graduate Students – Michael Stone – 1st Edition


An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables.

The authors’ exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study.

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  • Preface
    1. Calculus of variations
    2. Function spaces
    3. Linear ordinary differential equations
    4. Linear differential operators
    5. Green functions
    6. Partial differential equations
    7. The mathematics of real waves
    8. Special functions
    9. Integral equations
    10. Vectors and tensors
    11. Differential calculus on manifolds
    12. Integration on manifolds
    13. An introduction to differential topology
    14. Group and group representations
    15. Lie groups
    16. The geometry of fibre bundles
    17. Complex analysis I
    18. Applications of complex variables
    19. Special functions and complex variables
  • Citation

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