Further Examples of Exactly Solvable ... (Mathematica Tutorial)

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

Overview of Linear Second-Order ODEs (Mathematica Tutorial)

Solving linear first-order ODEs is straightforward and only requires the use of a suitable integrating factor. In sharp contrast, there are a large number of methods ...

Introduction to Systems of ODEs (Mathematica Tutorial)

Systems of ODEs are important in various fields of science, such as the study of electricity and population biology. Like single ODEs, systems of ODEs can classified as ...

Linear First-Order Equations (Mathematica Tutorial)

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

Euler and Legendre Equations (Mathematica Tutorial)

An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.

Manipulating Integrals in Symbolic Form (Mathematica Tutorial)

When Mathematica cannot give you an explicit result for an integral, it leaves the integral in a symbolic form. It is often useful to manipulate this symbolic form. ...

Random Number Generation (Mathematica Overview)

Introduction Random Generation Functions Seeding and Localization

Scalars, Vectors, and Matrices (Mathematica Tutorial)

Mathematica represents matrices and vectors using lists. Anything that is not a list Mathematica considers as a scalar. A vector in Mathematica consists of a list of scalars. ...

Unconstrained Optimization (Mathematica Overview)

Introduction Methods for Local Minimization Methods for Solving Nonlinear Equations

Built-in Graphs (Combinatorica Package Guide)