The second edition of Advanced Methods of Mathematical Physics has been considerably revised, enlarged and updated. This is typically a two-semester course material for students pursuing Master’s degree programs in theoretical physics and mathematics covering such topics as the theory of finite groups, introductory topology and differential geometry, integral equations, Sturm-Liouvilles’s theory including Green’s functions, stochastic processes and stochastic differential equations, nonlinear dynamics, solution of nonlinear differential and integral equations, symmetries of differential equations and normal modes in nonlinear dynamical systems. What the anvil means to the blacksmith, what a car means to the businessman, what a violin means to the musician, that’s what mathematics means to a theoretical physicist. Not only can we not live without it. We love mathematics. We play with it even in the rare cases that we do not need it. Mathematics is fun. Students in theoretical physics need good teachers and good books to learn mathematics. Here is such a book. Devour. Enjoy Gerardus ‘t Hooft Noble Laureate Professor of Physics, University of Utrecht, The Netherlands ……….an extremely useful textbook. I am sure that it will be much used by many students. James D. Bjorken Professor of Physics, Stanford Linear Accelerator Center, Stanford University, USA NEW TO THE SECOND EDITION: • Two appendices: - on differentiation and integration under the integral sign - on the existence of the limit cycles in a Lienard system • New examples as also some additional pertinent problems listed at appropriate places in the text

General Introduction / Theory of Finite Group / Rudiments of Topology and Differential Geometry / Integral Equations, Sturm-Liouville Theory and Green’s Functions / Stochastic Processes and Stochastic Differential Equations / Methods of Nonlinear Dynamics I: Phase Portraits / Methods of Nonlinear Dynamics II: Stability and Bifurcation / Some Nonlinear Differential Equations and their Solutions / Some Nonlinear Integral Equations and their Solutions / Exact Solution of Some Nonlinear Differential Equations / Symmetries of Differential Equations / Normal Modes in Nonlinear Dynamical Systems / Appendix A: Some Numerical Aspects of Nonlinear Dynamical Systems Vis-à-vis Chaos / Appendix B: Differentiation and Integration under the Integral Sign / Appendix C: Further Remarks on the Existence of Limit Cycles in a Lienard System / Bibliography / Index.

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