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.
This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain 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.
Kevin Brown's compilation of postings including many topics in differential equations.
A web text on the background to the extrapolation method for the numerical solution of elliptic boundary value problems by Kwok Sui-Yuen Billy.
A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
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.
A set of lecture notes on Poisson's equation. [PDF Format]
A set of lecture notes on Green's functions and their applications.
A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
Science /
Math /
Calculus
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