Richard H. Enns - Böcker

Computer algebra systems have revolutionized the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. This self-contained text is organized along a spiral, revisiting the general topics of graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral. The heart of this text is a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE not only to provide tools for problem solving, but also to stimulate the readers imagination. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. A scientific model or method is associated with each recipe, along with an interesting or amusing story to help maintain the readers interest. All recipes are included on the CD-ROM enclosed with the book.Aimed at first- and second-year science and engineering undergraduates, the presentation is driven by examples from a variety of disciplines to appeal to students in mathematics, physics, engineering, chemistry, economics, biology, and pre-medicine. The spiral design allows the book to be effectively used as a computational science text: each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further. Computer Algebra Recipes: An Introductory Guide to Mathematical Modeling may also be used for self-study and may form the basis of an on-line course.

Modern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. This self-contained text benefits from a spiral structure that regularly revisits the general topics of graphics, symbolic computation, and numerical simulation with increasing intricacy at each turn. The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. Each recipe is associated with a scientific model or method and an interesting or amusing story designed to both entertain and enhance concept comprehension and retention. All recipes are included on the CD-ROM enclosed with the book.Aimed at third- and fourth-year undergraduates in science and engineering, the text contains numerous examples in disciplines that will challenge students progressing in mathematics, physics, engineering, game theory, and physical chemistry. Computer Algebra Recipes: An Advanced Guide to Mathematical Modeling can serve as an effective computational science text, with a set of problems following each section of recipes to enable readers to apply and confirm their understanding. The book may also be used as a reference, for self-study, or as the basis of an on-line course.

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations.After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations.  No prior knowledge of Maple is assumed.Thebook may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.

Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies.

Science demands that all theory must be checked by experiment. Richard Feyn­ man, Nobel Laureate in physics (1965), reminds us in a wonderful quote that "The test of all knowledge is experiment. Experiment is the sole judge of sci­ entific truth. " 1 It is because nonlinear physics can be so profoundly counter­ intuitive that these laboratory investigations are so important. This manual is designed to be used with the text Nonlinear Physics with Maple for Scientists and Engineers. Understanding is enhanced when experiments are used to check so please attempt as many of the activities as you can. As you perform theory, these activities, we hope that you will be amazed and startled by strange behav­ ior, intrigued and terrorized by new ideas, and be able to amaze your friends as you relate your strange sightings! Remember that imagination is just as impor­ tant as knowledge, so exercise yours whenever possible. But please be careful, as nonlinear activities can be addicting, can provide fond memories, and can awaken an interest that lasts a lifetime. Although it has been said that a rose by any other name is still a rose, (with apologies to Shakespeare) the authors of this laboratory manual have, in an endeavor to encourage the use of these nonlinear investigations, called them experimental activities rather than experiments. A number of design innovations have been introduced: A.

Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, phys­ ics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software sys­ tem applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non­ linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of "hands on" experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated.

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. The authors have included a CD-ROM that contains over 130 annotated Mathematica files. These files may be used to solve and explore the text's 400 problems. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

This work may be used as a source for algebra "recipes" for second year undergraduates. The book does not try to teach the fundamentals of the subject, rather the recipes are organised to correlate with topics found in standard classical mechanics texts. The book utilises the computer algebra system MAPLE (Release 7) but no prior knowledge of MAPLE is presumed. The relevant command structures are explained on a need-to-know basis as the recipes are developed thus making this a standalone text. The computer algebra recipes are introduced in the context of interesting tales and have been placed on a Windows Platform CD that accompanies the book. Mac and UNIX systems are also compatible. The CD also includes computer algebra solutions to hundreds of problems. This problem-solving guide can be used in a variety of ways: a classroom text, a reference text, a text for an on-line course, or as a self-study guide. It will benefit science professionals and engineers who need to quickly solve complex classical mechanics problems relevant to their work and it should prove useful for instructors seeking a modern approach to teaching the subject.

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, phys­ ics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software sys­ tem applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non­ linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of "hands on" experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated.

The Advanced Study Institute (ASI) on Nonlinear Phenomena-in Physics and Biology was held at the Banff Centre, Banff, Alberta, Canada, from 17 - 29 August, 1980. The Institute was made possible through funding by the North Atlantic Treaty Organization (who sup­ plied the major portion of the financial aid), the National Research and Engineering Council of Canada, and Simon Fraser University. The availability of the Banff Centre was made possible through the co­ sponsorship (with NATO) of the ASI by the Canadian Association of Physicists. 12 invited lecturers and 82 other participants attended the Institute. Except for two lectures on nonlinear waves by Norman Zabusky, which were omitted because it was felt that they already had been exhaustively treated in the available literature, this volume contains the entire text of the invited lectures. In addition, short reports on some of the contributed talks have also been included. The rationale for the ASI and this resulting volume was that many of the hardest problems and most interesting phenomena being studied by scientists today ar.e nonlinear in nature. The nonlinear models involved often span several different disciplines, °a simple example being the Volterra-type model in population dynamics which has its analogue in nonlinear optics and plasma physics (the 3-wave problem), in the discussion of the social behavior of animals, and in biological competition and selection at the molecular level.