A Set of Appendices on Mathematical Methods for Physics Students
by Anne Fry, Amy Plofker, Sarah-marie Belcastro
Number of pages: 90
90-page document covering useful mathematical background for physics students at all undergraduate levels. Topics: Matrices, Eigenvalues and Eigenvectors, Intro To Differential Equations, Integration, Proofs by Induction, Fourier Analysis and Transforms, Converting Sums to Integrals, Unit Systems, etc.
This document is no more available for free.
by Eric L. Michelsen - UCSD
This text covers some of the unusual or challenging concepts in graduate mathematical physics. This work is meant to be used with any standard text, to help emphasize those things that are most confusing for new students.
by Sergiu I. Vacaru - arXiv
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces.
by Peter B. Gilkey - Publish or Perish Inc.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas and the Gauss-Bonnet theorem.
by Boris Dubrovin - SISSA
These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.