Solving Linear Systems (Mathematica Tutorial)

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

Advanced Numerical Differential ... (Mathematica Tutorial)

[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. ...

ContourPlot (Built-in Mathematica Symbol)

ContourPlot[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a contour plot of f as a function of x and y. ContourPlot[f == g, {x, x_min, x_max}, {y, y_min, y_max}] plots ...

Verification of the Solution (Mathematica Tutorial)

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

BesselJ (Built-in Mathematica Symbol)

BesselJ[n, z] gives the Bessel function of the first kind J_n (z).

String Representation of Boxes (Mathematica Tutorial)

Mathematica provides a compact way of representing boxes in terms of strings. This is particularly convenient when you want to import or export specifications of boxes as ...

Atomic Elements of Expressions (Mathematica Guide)

All expressions in Mathematica are ultimately built from a small number of distinct types of atomic elements.

HaarWavelet (Built-in Mathematica Symbol)

HaarWavelet[] represents a Haar wavelet.

CoifletWavelet (Built-in Mathematica Symbol)

CoifletWavelet[] represents a Coiflet wavelet of order 2.CoifletWavelet[n] represents a Coiflet wavelet of order n.

Functions of Complex Variables (Mathematica Guide)

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...