Differential equations relate functions of several variables to derivatives of the functions. Such equations are often used in the sciences to relate a quantity to its rate of change.

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Analytic Differential Equations

Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute.
[PDF]

The Animated Telegraph equation

This demonstration illustrates the behaviour of solutions of the telegraph equation

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.

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.

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

"PDE Primer" by Ralph Showalter at Oregon State.

Partial Differential Equations

Maple lessons for an undergraduate course in Differential Equations by Jim Herod.

Partial Differential Equations

Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.

Partial Differential Equations

An overview of partial differential equations and their physical applications.

The Polar Representation Theorem

An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon.
[PDF]

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 World of Mathematical Equations

Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.

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