Mathematica by Example bridges the gap that exists between the very elementary handbooks available on Mathematica and those reference books written for the advanced Mathematica users. Mathematica by Example is an appropriate reference for all users of Mathematica and, in particular, for beginning users like students, instructors, engineers, business people, and other professionals first learning to use Mathematica. Mathematica by Example introduces the very basic commands and includes typical examples of applications of these commands. In addition, the text also includes commands useful in areas such as calculus, linear algebra, business mathematics, ordinary and partial differential equations, and graphics. In all cases, however, examples follow the introduction of new commands. Readers from the most elementary to advanced levels will find that the range of topics covered addresses their needs.
Taking advantage of Version 11 of Mathematica, Mathematica by Example, Fifth Edition, introduces the fundamental concepts of Mathematica to solve typical problems of interest to students, instructors, and scientists. The Fifth Edition is an extensive revision of the text. Features that make Mathematica by Example, Fifth Edition, as easy to use as a reference and as useful as possible for the beginner include the following.
1. Version 11 Compatibility. All examples illustrated in Mathematica by Example, Fifth Edition, were completed using Version 11 of Mathematica. Although many computations can continue to be carried out with earlier versions of Mathematica, we have taken advantage of the new features in Version 11 as much as possible.
2. Applications. New applications, many of which are documented by references, from a variety of fields, especially biology, physics, and engineering, are included throughout the text. Especially notice the new examples regarding series in Chapter 3 and manipulation of photographs in Chapters 2, 4, and 5.
3. Detailed Table of Contents. The table of contents includes all chapter, section, and subsection headings. Along with the comprehensive index, we hope that users will be able to locate information quickly and easily.
4. Additional examples. We have considerably expanded the topics in Chapters 1 through 6. The results should be more useful to instructors, students, business people, engineers, and other professionals using Mathematica on a variety of platforms.
5. Comprehensive Index. In the index, mathematical examples and applications are listed by topic, or name, as well as commands along with frequently used options: particular mathematical examples as well as examples illustrating how to use frequently used commands are easy to locate. In addition, commands in the index are cross-referenced with frequently used options. Functions available in the various packages are cross-referenced both by package and alphabetically.
6. As technology has changed, so has the publication of a book. When Mathematica by Example was first published in 1992, it was published as a single color book. Consequently, at that time, it was important to use various gray levels in plots to help distinguish them. Now, many of you will download an electronic copy of the text and print it on a high-resolution color printer with high-quality paper. The result will be outstanding. To illustrate the use of color, we have chosen from various universities and colleges throughout the United States. We tried to use the colors from at least one university or college in each state. Sometimes this was difficult to do because obtaining the color codes from some colleges was easier than from others. Of course, in the print version of the text, all images will still be in various levels of gray.
We began Mathematica by Example in 1990 and the first edition was published in 1991. Back then, we were on top of the world using Macintosh IIcx's with 8 megs of RAM and 40 meg hard drives. We tried to choose examples that we thought would be relevant to beginning users – typically in the context of mathematics encountered in the undergraduate curriculum. Those examples could also be carried out by Mathematica in a timely manner on a computer as powerful as a Macintosh IIcx.
When working on the Fifth edition, we are on the top of the world with iMacs with dual Intel processors complete with 8 gigs of RAM and 1 or 2 Terabyte hard drives. Now we are working with machines with more memory than we can comprehend and so fast we can't believe that computers will be faster but they will almost certainly be nearly obsolete by the time you are reading this. The examples presented in Mathematica by Example continue to be the ones that we think are most similar to the problems encountered by beginning users and are presented in the context of someone familiar with mathematics typically encountered by undergraduates. However, for this Fifth edition of Mathematica by Example we have taken the opportunity to expand on several of our favorite examples because the machines now have the speed and power to explore them in greater detail.
Other improvements to the Fifth edition include:
1. In Chapter 3, we have increased the number of examples relating to applications of series, particularly discussing “how is π approximated accurately now?”
2. Chapter 4, Introduction to Lists and Tables, contains several examples illustrating various techniques of how to quickly create plots of bifurcation diagrams, Julia sets, and the Mandelbrot set with new Mathematica functions that make visualizing these sets remarkably easy.
3. In Chapter 6, we have taken advantage of the Manipulate function to illustrate a variety of situations and expand on many examples throughout the chapter. For example, see Example 6.13 for a comparison of solutions of nonlinear equations to their corresponding linear approximations.
4. We have included references that we find particularly interesting in the Bibliography, even if they are not specific Mathematica-related texts. A comprehensive list of Mathematica-related publications can be found at the Wolfram web site.
http://store.wolfram.com/catalog/books/
Also, be sure to investigate, use, and support Wolfram's MathWorld – simply an amazing web resource for mathematics, Mathematica, and other information.
http://store.wolfram.com/catalog/books/
June, 2017