Differential Equations

Green's Function Library - Collection of Green's function solutions to canonical differential equations.
http://www.engr.unl.edu/~glibrary/

Green's Function Theory - A set of lecture notes on Green's functions and their applications.
http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node59.html

PRIDE - Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
http://www.amsta.leeds.ac.uk/Applied/CAGD.dir/PRIDE/index.htm

Difference Method for Numerical Approximation to Applied Differential Equations. - This page explains how to use the difference formula of differentials to approximate the differential equations for applied systems. This method is used when analytical techniques are unavailable or cause computers to spit out garbage. This difference method is very similar to the Runge-Kata and Newton's method.
http://www.geocities.com/b_ward.rm/na.html

Introduction to Green's Functions - Green's functions play an important role in the solution of linear ordinary and partial differential equations, and are a key component to the development of boundary integral equation methods.
http://www.boulder.nist.gov/div853/greenfn/tutorial.html

Partial Differential Equations - "PDE Primer" by Ralph Showalter at Oregon State.
http://www.math.oregonstate.edu/~show/docs/pde.html

Analytic Differential Equations - Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute. [PDF]
http://www.wisdom.weizmann.ac.il/~yakov/thebook.pdf

MathPages: Calculus and DiffEq Notes - Kevin Brown's compilation of postings including many topics in differential equations.
http://www.mathpages.com/home/icalculu.htm

Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.
http://math.ucsd.edu/~driver/231-02-03/lecture_notes.htm

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.
http://home.comcast.net/~cmdaven/korteweg.htm

The Polar Representation Theorem - An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. [PDF]
http://gfm.cii.fc.ul.pt/people/jrezende/jr_polar-repr.pdf

Partial Differential Equations - An overview of partial differential equations and their physical applications.
http://www.cmth.ph.ic.ac.uk/people/a.mackinnon/Lectures/compphys/node24.html

Ordinary Differential Equations - Course notes by Klaus Schmitt at the University of Utah.
http://www.math.utah.edu/~schmitt/math6410.html

Differential Equations in a Nutshell - An overview of the terms used, as well as solving general and initial value problems. Includes corresponding graphs. [PDF]
http://spot.pcc.edu/~ssimonds/m253/week_6/MTH_253_diffy_Q_200602.pdf

MGNet - Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
http://www.mgnet.org/

arXiv Front: AP Analysis of PDEs - PDEs section of the mathematics e-print arXiv.
http://front.math.ucdavis.edu/math.AP

The Animated Telegraph equation - This demonstration illustrates the behaviour of solutions of the telegraph equation
http://www.math.ubc.ca/~feldman/demos/demo8.html

Weak and Variational Forms of Poisson's Equation - A set of lecture notes on Poisson's equation. [PDF]
http://caswww.colorado.edu/courses.d/AFEM.d/AFEM.Ch03.d/AFEM.Ch03.pdf

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.
http://www.coolissues.com/mathematics/Navier-Stokes/nstokes.htm

Table of Laplace Transforms - This page includes an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
http://www.vibrationdata.com/Laplace.htm

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.
http://www.maths.gla.ac.uk/~ca/

Computational PDEs Unit - School of Computing, University of Leeds. Research details, publications, software and resources.
http://www.scs.leeds.ac.uk/cpde/

Differential Equations in Banach Algebras - Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal. [PDF]
http://www.gwfa.de/math/Fuchs_1996.pdf

The World of Mathematical Equations - Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.
http://eqworld.ipmnet.ru/

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, ...).
http://www.geuz.org/getdp/

C*ODE*E Archive - Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
http://www.math.hmc.edu/codee/

Elliptic Problems with Concentrated Loading - A web text on the background to the extrapolation method for the numerical solution of elliptic boundary value problems by Kwok Sui-Yuen Billy.
http://www.sci.hkbu.edu.hk/mscsc/dissert/billy/node1.html

Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses - Online course material
http://math.bu.edu/DYSYS/ode-bif/ode-bif.html

Differential Equations - Postscript notes on various topics in differential equations by Bruce Ikenaga.
http://marauder.millersville.edu/~bikenaga/diffeq/deqnote.html

Partial Differential Equations - Maple lessons for an undergraduate course in Differential Equations by Jim Herod.
http://www.mapleapps.com/powertools/pdes/pdes.shtml

Math Unit III: More on the derivative and differential equations - Exact definition of derivation and calculating the relationship of derivatives of related functions.
http://dept.physics.upenn.edu/courses/gladney/mathphys/subsection3_1_1.html

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.
http://home.comcast.net/~cmdaven/burgers.htm

Differential Equations in Industry and Commerce - European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.
http://www.maths.ox.ac.uk/ociam/TMR/

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.
http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node2.html

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.
http://www.mathphysics.com/pde/green/g15.html