Elements for Physics: Quantities, Qualities, and Intrinsic Theories
by Albert Tarantola
Publisher: Springer 2006
Number of pages: 280
The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
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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 Herbert S Wilf - Dover Publications
The book for the advanced undergraduates and graduates in the natural sciences. Vector spaces and matrices, orthogonal functions, polynomial equations, asymptotic expansions, ordinary differential equations, conformal mapping, and extremum problems.
by S.R.S. Varadhan - Tata Institute of Fundamental Research
Starting from Brownian Motion, the lectures quickly got into the areas of Stochastic Differential Equations and Diffusion Theory. The section on Martingales is based on additional lectures given by K. Ramamurthy of the Indian Institute of Science.
by Cathleen S. Morawetz - Tata Institute Of Fundamental Research
Introduction to certain aspects of gas dynamics concentrating on some of the most important nonlinear problems, important not only from the engineering or computational point of view but also because they offer great mathematical challenges.