Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

In this tutorial, the following topics are discussed: The following sequence explains how to use the Reshape tool ( GraphicsBox[RasterBox[CompressedData[ ], {Offset[{0.5, ...

Patterns are used throughout Mathematica to represent classes of expressions. A simple example of a pattern is the expression f[x_]. This pattern represents the class of ...

Once installed, MathLM starts running automatically by default each time the machine is rebooted. To start or stop MathLM manually, follow these instructions. It is assumed ...

With the default option setting Lighting->Automatic, Mathematica uses a simulated lighting model to determine how to color polygons in three-dimensional graphics. Mathematica ...

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 ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language ...

A full Mathematica installation consists of thousands of separate files, arranged in several hundred directories under the main installation directory. The location of the ...