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• Science: Math: Calculus  (88)
• Science: Physics: Mathematical Physics  (218)

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




» 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.




» 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.




» Differential Equations - Postscript notes on various topics in differential equations by Bruce Ikenaga.




» Differential Equations in a Nutshell - An overview of the terms used, as well as solving general and initial value problems. Includes corresponding graphs. [PDF]




» Differential Equations in Banach Algebras - Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal. [PDF]




» Differential Equations in Industry and Commerce - European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.




» 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.




» 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.




» 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.




» 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.




» Math Unit III: More on the derivative and differential equations - Exact definition of derivation and calculating the relationship of derivatives of related functions.




» 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.




» Ordinary Differential Equations - Course notes by Klaus Schmitt at the University of Utah.




» 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 - An overview of partial differential equations and their physical applications.




» Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.




» 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.




» Weak and Variational Forms of Poisson's Equation - A set of lecture notes on Poisson's equation. [PDF]




» The World of Mathematical Equations - Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.