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 Science: Math: Applications
Science: Math: Topology
Burger's Equation
An applet demonstrating Burger's equation in one dimension.
Burger's Equation
An overview of the simplest differential equation which allows for shocks and other discontinuities.
Celestial Mechanics Research
Links, animations, references, and a brief description of research into n-body problems.
Clyde Davenport's Commutative Hypercomplex Mathematics
Summary and application as it relates to electromagnetic theory and special relativity.
Complex Geometry of Nature and General Relativity
A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
Differential Equations and Oscillations
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.
Dimensional Analysis
A simple review of the powerful technique of dimensional analysis.
The Dirac Delta Function
A brief introduction to the properties and uses of the Dirac delta function.
Discrete Self-trapping Equation
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
Doing Physics with Quaternions
A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
Elastic Strain Soliton Visualization
Windows demonstration program download.
Euclidean Geometric Transforms for Physics
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.
Five Lectures on Soliton Equations
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
Holomorphic Methods in Mathematical Physics
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.
Homological Methods in Mathematical Physics
These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.
Inexplicable Secrets of Creation
Relationships between number theory and physics.
An Introduction to Noncommutative Geometry
A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
Kinetic Theory and its Applications.
This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry.
Lectures on Orientifolds and Duality
Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
Local Quantum Physics Crossroads
An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).
Non Commutative Geometry
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
Open Problems in Mathematics and Physics
Links to open problems in mathematics, physics and other subjects.
Orthogonal Polynomials and Multilevel Systems Dynamics
We study multiphoton excitation of molecules by infrared laser radiation. We try to find analytic solutions of the dynamic equations using miscellaneous orthogonal polynomials (Gegenbauer, Jacobi, Pollaczek, Laguerre, Meixner, Krawtchouk, Hahn etc.).
Radial Symmetric Fourier Transforms
Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Illustrations of the method are presented, and of the Gibbs' phenomenon.
Recent Developments in Skyrme Models
An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.
Solitons
Resources at Heriot-Watt University. Meetings, local and other links.
Solitons
An overview of the classical and quantum theory related to solitons
Symplectic Geometries in Quantum Physics and Optics
A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
This Week's Finds in Mathematical Physics
This is a column written about modern topics in mathematical physics.
Topology and Physics
An essay by C. Nash on the historical connection between topology and physics.
Twistor Web
A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. Some papers on-lin.
Twistors- What are they?
A set of notes introducing spinors and twistors.
Visual Mathematical Physics
Collection of animated gif pictures describing the solutions of the main partial differential equations such as Laplace, Poisson, string and membrane oscillations and heat conduction.
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