Introduction

No book is born in a vacuum. There must always be somebody who needs the book, somebody who will read and use it, and somebody who will write it. I walked with the idea of this book for a long time. However, its final concept came into reality during my lectures, in February 2005, at the Universiti Malaysia Sabah in Borneo. I realized that my students needed a bit more than just my lectures. They needed a text that they could follow during lab sessions or after classes so they could learn at any time, at their own pace. Therefore, I decided to write a small book with just a few chapters covering the different areas of applying the Computer Algebra System called MuPAD in different areas of mathematics. I intended each chapter to be short enough to be covered in a reasonably short time, about 2 to 4 hours.

Another important objective was to have each chapter completely independent of the others, so that the readers could easily select and read the chapters that they needed the most, without being forced to read the whole book. There was one obstacle for such a concept—the large number of graphics I used to visualize mathematics. Therefore, I finally decided to write a separate chapter covering the major concepts of MuPAD graphics. The graphics chapter, together with the introductory chapter, forms the base for all the remaining chapters. Therefore, chapters 1 and 2 should be read first and foremost, but the remaining chapters can be read in any order.

Allow me to mention what you will find in this book. Chapter 1 is the introductory chapter, and it covers some very basic information about MuPAD. You should read this chapter if you do not know anything about MuPAD. The second chapter contains a reasonably brief description of the concept of MuPAD graphics, and introduces the Virtual Camera tool and the major types of graphical objects. Chapters 3 and 4 are devoted to calculus of one variable and several variables, respectively; they require a basic knowledge of calculus. This book isn’t intended to teach mathematics; it teaches only how to apply MuPAD in mathematics. Chapter 5 is devoted to working with selected algebraic concepts with MuPAD. Chapter 6 shows how MuPAD can be used in elementary statistics and in the visualization of discrete data. Finally, chapter 7 introduces some basic programming concepts in MuPAD.

The chapters in this book aren’t intended to cover specific mathematical disciplines in detail. However, the book gives the readers enough basic knowledge to start using MuPAD in several disciplines. Readers who are interested in a more detailed book on programming with MuPAD may read my MuPAD Pro Computing Essentials, which focuses on programming and using MuPAD programs in mathematics. I know that there are many other mathematical disciplines that are worth exploring with MuPAD. Perhaps one day I, or somebody else, will write the missing chapters on analytic geometry, number theory, abstract algebra, discrete mathematics, and so on. Finally, I know also that each chapter of this book could be the staring point for a new exciting textbook for a regular college or university course. For example, writing a textbook for a course on abstract algebra or discrete mathematics with MuPAD could be a very fascinating project. Therefore, this book is not only a collection of MuPAD workshops, but also can be considered as a starting point for many interesting new projects.

I am very grateful to Prof. Fred Szabo and Prof. Bernard Liengme as well as to my son Jakub for proofreading and commenting on the manuscript of this book. I thank them for their wonderful support and for the time they spent helping me in this project. The first two chapters of this book were used during my lectures at Mumbai University in April 2005, and they were received with great enthusiasm by my colleagues and the participants in my lectures.

The manuscript of this book, as well as all other my books, was written using Scientific Workplace, the best tool ever made for writing mathematical texts and experimenting with mathematics. I would like to thank Barry MacKichan and his excellent team for creating Scientific Workplace and for their never ending support of my work.

Miroslaw Majewski, Zayed University, June 2005

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