Phy.org - Science: Math: Differential Equations

Analytic Differential Equations - Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute.
Analytic Solution for the Burgers Equation - Provides the general analytic solution for the Burgers equation in the form of a 4-D commutative hypercomplex function. The solution exhibits the main dynamic features in a Burgers medium: propagation of disturbances, shock waves, propagating state change fronts, and solitons. Includes page about hypercomplex math.
Analytical solution for the Korteweg-de Vries equation - Provides the general analytic solution for the KdV equation. In one function, the result models traveling wavetrains, solitary spikes (solitons), and sech-form long waves.
arXiv Front: AP Analysis of PDEs - PDEs section of the mathematics e-print arXiv.
Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses - Online course material
C*ODE*E Archive - Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
Complex Analysis and Dynamics - Various lecture notes by C. McMullen
Computational PDEs Unit - School of Computing, University of Leeds. Research details, publications, software and resources.
Differential Equations in Banach Algebras - Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal.
Finding Green's Functions for ODEs - A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
GetDP (a General environment for the treatment of Discrete Problems) - A scientific software environment for the numerical solution of integro-differential equations, open to the coupling of physical problems (electromagnetic, acoustic, thermal, mechanical, ...) as well as of numerical methods (finite element methods, boundary element and integral methods, ...).
Green's Function Library - Collection of Green's function solutions to canonical differential equations.
Green's Function Theory - A set of lecture notes on Green's functions and their applications.
Linear Mathematics in Infinite Dimensions - A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
MathPages: Calculus and DiffEq Notes - Kevin Brown's compilation of postings including many topics in differential equations.
MGNet - Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
Navier-Stokes Type Equations - Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
Nonlinear Differential Equations at Glasgow - The site describes research activities of the differential equations group in the mathematics department at the university of Glasgow, UK, and provides some resources of a general nature.
Partial Differential Equations - Maple lessons for an undergraduate course in Differential Equations by Jim Herod.
Partial Differential Equations - An overview of partial differential equations and their physical applications.
Partial Differential Equations - "PDE Primer" by Ralph Showalter at Oregon State.
Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.
PRIDE - Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
Table of Laplace Transforms - This page includes an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
The Animated Telegraph equation - This demonstration illustrates the behaviour of solutions of the telegraph equation
The Polar Representation Theorem - An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon.
The World of Mathematical Equations - Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.
Weak and Variational Forms of Poisson's Equation - A set of lecture notes on Poisson's equation.

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