Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

Using the objects described in "Introduction to Patterns", you can set up patterns for many kinds of expressions. In all cases, you must remember that the patterns must ...

New function SemialgebraicComponentInstances has been added to the built-in Mathematica kernel.

Mathematica provides tools to simplify a diverse range of mathematical expressions to make them easier to understand, or more efficient to compute.

Introduction ODE Integration Methods Partial Differential Equations

This package provides an interactive tool for investigating the solutions of differential equations as well as other types of equations that have solutions that can be viewed ...

Constructing Matrices Getting and Setting Pieces of Matrices Scalars, Vectors, and Matrices

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...

ProductLog[z] gives the principal solution for w in z == w e^w. ProductLog[k, z] gives the k\[Null]^th solution.