Wednesday, July 17, 2019

Applied Mathematical Methods in Theoretical Physics

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This book on integral equations and the calculus of variations is intended for use by senior undergraduate students and first-year graduate students in science and engineering. Basic familiarity with theories of linear algebra, calculus, differential equations, and complex analysis on the mathematics side, and classical mechanics, classical electrodynamics, quantum mechanics including the second quantization, and quantum statistical mechanics on the physics side, is assumed. Another prerequisite for this book on the mathematics side is a sound understanding of local and global analysis.

This book grew out of the course notes for the last of the three-semester sequence of Methods of Applied Mathematics I (Local Analysis), II (Global Analysis) and III (Integral Equations and Calculus of Variations) taught in the Department of Mathematics at MIT. About two-thirds of the course is devoted to integral equations and the remaining one-third to the calculus of variations. Professor Hung Cheng taught the course on integral equations and the calculus of variations every other year from the mid 1960s through the mid 1980s at MIT. Since then, younger faculty have been teaching the course in turn. The course notes evolved in the intervening years. This book is the culmination of these joint efforts.

1. Function Spaces, Linear Operators and Green’s Functions
2. Integral Equations and Green’s Functions
3. Integral Equations of Volterra Type
4. Integral Equations of the Fredholm Type
5. Hilbert–Schmidt Theory of Symmetric Kernel
6. Singular Integral Equations of Cauchy Type
7. Wiener–Hopf Method and Wiener–Hopf Integral Equation
8. Nonlinear Integral Equations
9. Calculus of Variations: Fundamentals
10. Calculus of Variations: Applications

Author Details
"Michio Masujima"

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