Equation Trekker Package (Equation Trekker Package Guide)

Logic & Boolean Algebra (Mathematica Guide)

Mathematica represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating ...

Inequalities (Mathematica Guide)

Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be ...

LogicalExpand (Built-in Mathematica Symbol)

LogicalExpand[expr] expands out logical combinations of equations, inequalities, and other functions.

FindRoot (Built-in Mathematica Symbol)

FindRoot[f, {x, x_0}] searches for a numerical root of f, starting from the point x = x_0.FindRoot[lhs == rhs, {x, x_0}] searches for a numerical solution to the equation lhs ...

Exact Linear Second-Order Equations (Mathematica Tutorial)

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

Inhomogeneous Linear Second-Order ... (Mathematica Tutorial)

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

Introduction to Partial Differential ... (Mathematica Tutorial)

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

Higher-Order Euler and Legendre ... (Mathematica Tutorial)

An Euler equation is an ODE of the form The following is an example of an Euler equation. The Legendre linear equation is a generalization of the Euler equation. It has the ...

Overview of Ordinary Differential ... (Mathematica Tutorial)

There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...