Mathematics for Physics: A Guided Tour for Graduate Students
by Michael Stone, Paul Goldbart
Publisher: Cambridge University Press 2009
Number of pages: 919
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.
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by G. 't Hooft, M. J. G. Veltman - Utrecht University
Contents: Quantum mechanics and rotation invariance; The group of rotations in three dimensions; More about representations; Ladder operators; The group SU(2); Spin and angular distributions; Isospin; The Hydrogen Atom; The group SU(3); etc.
by John C. Baez, Mike Stay - arXiv
There is extensive network of analogies between physics, topology, logic and computation. In this paper we make these analogies precise using the concept of 'closed symmetric monoidal category'. We assume no prior knowledge of category theory.
by Albert Tarantola - Springer
Reviews Lie groups, differential geometry, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. The theory of heat conduction and the theory of linear elastic media are studied in detail.
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.