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 ...

The Syntax of the Mathematica Language (Mathematica Tutorial)

Mathematica uses various syntactic rules to interpret input that you give, and to convert strings and boxes into expressions. The version of these rules that is used for ...

Computational Geometry (Mathematica Guide)

Mathematica's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making ...

The Design of the NDSolve Framework (Mathematica Tutorial)

Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

MathieuCPrime (Built-in Mathematica Symbol)

MathieuCPrime[a, q, z] gives the derivative with respect to z of the even Mathieu function with characteristic value a and parameter q.

MathieuSPrime (Built-in Mathematica Symbol)

MathieuSPrime[a, q, z] gives the derivative with respect to z of the odd Mathieu function with characteristic value a and parameter q.

Integrate (Built-in Mathematica Symbol)

Integrate[f, x] gives the indefinite integral \[Integral]f d x. Integrate[f, {x, x_min, x_max}] gives the definite integral \[Integral]_x_min^x_max\ f\ d x. Integrate[f, {x, ...

PolynomialExtendedGCD (Built-in Mathematica Symbol)

PolynomialExtendedGCD[poly_1, poly_2, x] gives the extended GCD of poly_1 and poly_2 treated as univariate polynomials in x.PolynomialExtendedGCD[poly_1, poly_2, x, Modulus ...

Mathieu and Related Functions (Mathematica Tutorial)

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...

Summary of New Features in Mathematica 8 (Mathematica Guide)