Lie Systems: Theory, Generalisations, and Applications
by J.F. Carinena, J. de Lucas
Publisher: arXiv 2011
Number of pages: 163
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule.
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by Pieter Naaijkens - arXiv
These are the lecture notes for a one semester course at Leibniz University Hannover. The main aim of the course is to give an introduction to the mathematical methods used in describing discrete quantum systems consisting of infinitely many sites.
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 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 Anne Fry, Amy Plofker, Sarah-marie Belcastro
Useful mathematical background for physics students at all undergraduate levels. Topics: Matrices, Eigenvalues and Eigenvectors, Intro To Differential Equations, Integration, Fourier Analysis and Transforms, Converting Sums to Integrals, etc.