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

Partial Differential Equations An overview of partial differential equations and their physical applications. www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node24.html

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. home.usit.net/~cmdaven/korteweg.htm

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. www.sci.hkbu.edu.hk/msc/full/billy/billy.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. www.mathphysics.com/pde/green/g15.html

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

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

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, bounda www.geuz.org/getdp

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

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

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

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

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

Numerical Methods for Partial Differential Equations Methods such as finite differences, finite elements, fast Fourier transforms, Monte-Carlo and Lagrangian schemes are discussed in 1D to solve a variety of problems including the advection, diffusion, Black-Scholes, Burger, Korteweg-DeVries and the Schroed www.fusion.kth.se/courses/pde

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

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

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 home.usit.net/~cmdaven/burgers.htm

Table of Laplace Transforms This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations. www.vibrationdata.com/Laplace.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 met www.geocities.com/b_ward.rm/na.html

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

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. www.boulder.nist.gov/div853/greenfn/tutorial.html

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

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

The Polar Representation Theorem An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format. gfm.cii.fc.ul.pt/Members/jr_polar-repr.pdf

PDEase2D 3.0 Solves partial differential equations numerically by finite element analysis for use in such problems as heat transfer, reaction diffusion, solid and fluid mechanics, electromagnetics, groundwater flow, and quantum mechanics. www.scientek.com/macsyma/pdmain.htm

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