MATHEMATICA NOTEBOOKS

Notebooks in the Atlas are designed to be used interactively as an essential aid for understanding the properties of functions. Thereby you can travel in the realms of applied mathematics, rather than making the journey vicariously by merely looking at static figures in a book.

      Graphical output for three-dimensional objects is illuminated by red, green, and blue lights, and the polygonal surfaces on the objects reflect light diffusely. Mathematica's default lighting and reflection directives are used.

      Many of the notebooks have cells, or parts of cells, that are program segments useful for generating algebraic expressions for functions in the text.  These are identified and annotated in each notebook.

      Messages generated by Mathematica within a given cell are sometimes allowed to appear, since they illustrate problems in computing the function in that cell. After you understand the reason for the message and have corrected the problem when feasible, you should probably use the Off[] function to suppress the message.

      The notebooks in the Web Atlas are compatible with Version 4.1 of Mathematica. They are usually compatible with Version 3.0 used in the Fortran-90 book version and with Version 2.2 used in the C book version.

Exploring with Notebook Cells 

Because the Atlas is designed to be used interactively, it is important to go exploring on your own. With every Mathematica cell in a notebook there will be suggestions on how to adapt the programs to see the functions from different viewpoints, or to compute different numerical and analytical properties.

      For example, the real part of the G function is depicted over the complex plane in the underlying motif. Its graphic object is computed by running cell GammaFunction in notebook GmBt. The chapter Gamma and Beta Functions has many different views of the gamma function—slices of surfaces, contour plots, and curves—and these may have stirred your interest to explore. Therefore each cell has suggestions modifying the program to see other aspects of the function. Thus, if you want to check out the poles of the G function at zero and the negative integers plot the function in more detail near the poles.

Notebook Annotations

Each cell in a Mathematica notebook in the Atlas is annotated. The main purpose of the annotations is to key the Mathematica code to equations, figures, and tables. Explanations of what the code is doing are given if appropriate. Definitions are distinguished from objects, and from surfaces, curves, or tables. Usually, all the definitions in a given cell appear before any are used. The order of definitions is graphics of surfaces and curves, followed by numerics.

Reliability of Programs: Disclaimer

All programs in the Atlas have been written carefully. Use of these programs is, however, at your own risk. The author and publisher disclaim all liability for direct or consequential damages resulting from use of the programs.