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Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses
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Online course material
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GetDP (a General environment for the treatment of Discrete Problems)
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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, ...).
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Nonlinear Differential Equations at Glasgow
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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.
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The Animated Telegraph equation
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This demonstration illustrates the behaviour of solutions of the telegraph equation
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Differential Equations in Industry and Commerce
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European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.
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arXiv Front: AP Analysis of PDEs
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PDEs section of the mathematics e-print arXiv.
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Computational PDEs Unit
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School of Computing, University of Leeds. Research details, publications, software and resources.
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Numerical Methods for Partial Differential Equations
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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 Schroedinger equations.
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Math Unit III: More on the derivative and differential equations
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Exact definition of derivation and calculating the relationship of derivatives of related functions.
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PRIDE
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Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
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Analytic Solution for the Burgers Equation
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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. A page is included to explain the hypercomplex mathematics.
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Table of Laplace Transforms
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This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
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Difference Method for Numerical Approximation to Applied Differential Equations.
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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.
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MathPages: Calculus and DiffEq Notes
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Kevin Brown's compilation of postings including many topics in differential equations.
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Elliptic Problems with Concentrated Loading
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A web text on the background to the extrapolation method for the numerical solution of elliptic boundary value problems by Kwok Sui-Yuen Billy.
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Finding Green's Functions for ODEs
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A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
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Introduction to Green's Functions
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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.
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Weak and Variational Forms of Poisson's Equation
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A set of lecture notes on Poisson's equation. [PDF Format]
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Green's Function Theory
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A set of lecture notes on Green's functions and their applications.
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Linear Mathematics in Infinite Dimensions
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A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
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Partial Differential Equations
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An overview of partial differential equations and their physical applications.
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The Polar Representation Theorem
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An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format.
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PDEase2D 3.0
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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.
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Navier-Stokes Type Equations
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Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
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Analytical solution for the Korteweg-de Vries equation
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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.
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Osaka University
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PDE-Analysis research group. Organises the East Asia Symposium on PDE.
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C*ODE*E Archive
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Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
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The World of Mathematical Equations
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Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.
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Differential Equations in Industry and Commerce
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EU TMR network coordinated at Oxford Centre for Industrial and Applied Mathematics.
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