The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

When you ask for the square root s of a number a, you are effectively asking for the solution to the equation s^2a. This equation, however, in general has two different ...

Mathematica is available for Windows, Linux, and Mac OS X. For a complete list of platform availability, visit www.wolfram.com/mathematica/features/system-requirements.html. ...

Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...

The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to ...

[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. ...

NIntegrate Introduction NIntegrate Integration Strategies NIntegrate Integration Rules

Expressions corresponding to notebooks. Here is a simple Mathematica notebook. Here is the expression that corresponds to this notebook.

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...

Cluster analysis is an unsupervised learning technique used for classification of data. Data elements are partitioned into groups called clusters that represent proximate ...