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Differential Equations and Oscillations - http://www.physics.orst.edu/~rubin/nacphy/ComPhys/DIFFEQ/mydif2/
Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations. |
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Mathematical Methods I - http://w3.physics.uiuc.edu/~m-stone5/mma/mma.html
This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign. |
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Hyperreal World - http://www.sun-inet.or.jp/~leibniz/math/
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese. |
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Solitons - http://physics1.usc.edu/~vongehr/solitons_html/solitons.html
An overview of the classical and quantum theory related to solitons |
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Five Lectures on Soliton Equations - http://arxiv.org/abs/q-alg/9712005
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type. |
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Topology and Physics - http://arxiv.org/abs/hep-th/9709135
An essay by C. Nash on the historical connection between topology and physics. |
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Holomorphic Methods in Mathematical Physics - http://arxiv.org/abs/quant-ph/9912054
This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. |
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Euclidean Geometric Transforms for Physics - http://physicstransforms.tripod.com/
A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas. |
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Commutative Hypercomplex Mathematics - http://home.comcast.net/~cmdaven/hyprcplx.htm
A commutative algebra, function theory, and system of analysis is developed for one 4-D variable (not quaternions). It is based upon a commutative group ring and extends all of the properties of the classical complex variables. |
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Non Commutative Geometry - http://dftuz.unizar.es/~rivero/research/index.html
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics. |