Richard H. Enns, George C. McGuire

Computer Algebra Recipes (eBook, PDF)

An Advanced Guide to Scientific Modeling

• Format: PDF

Produktbeschreibung

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 online course.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 374
• Englisch
• ISBN-13: 9780387493336
• Artikelnr.: 43728609

Autorenporträt

Richard H. Enns, Simon Fraser University, Burnaby, BC, Canada / George C. McGuire, University College of the Fraser Valley, Abbotsford, BC, Canada

Inhaltsangabe

From the contents: Introduction: 0.1. Computer Algebra Systems. 0.2. The Spiral Staircase to Learning. 0.3. How to Climb the Spiral Staircase.-I. THE APPETIZERS: 1. The Pictures of Science: 1.1. Introduction. 1.2. Data and Function Plots: 1.2.1. Correcting for Inflation; 1.2.2. The Plummeting Badminton Bird; 1.2.3. Minimizing the Travel Time. 1.3. Log-log (Power Law) Plots: 1.3.1. Chimpanzee Brain Size; 1.3.2. Scaling Arguments and Gulliver's Travels. 1.4. Contour and Gradient Plots: 1.4.1. The Secret Message; 1.4.2. Designing a Ski Hill. 1.5. Animated Plots: 1.5.1. Waves are Dynamic; 1.5.2. The Sands of Time.2. Deriving Model Equations: 2.1. Introduction. 2.2. Linear Correlation: 2.2.1. What is Linear Correlation? 2.2.2. The Corn Palace. 2.3. Lease Squares Derivation of Model Equations: 2.3.1. Regression Analysis; 2.3.2. Will You Be Better Off Than Your Parents? 2.3.3. What was the Heart Rate of a Brachiosaurus? 2.3.4. Senate Renewal; 2.3.5. Bikini Sales and the Logistic Curve; 2.3.6 Following the Dow Jones Index; 2.3.7. Variation of 'g' with Latitude; 2.3.8. Finding Romeo a Juliet. 2.4. Deriving Multiple Regression.

Rezensionen

From the reviews:

"Computer Algebra Recipes . . . is an eclectic collection of application stories together with associated Maple computer algebra worksheets or recipes. . . . The authors have designed this book to show how a computer algebra system such as Maple can be a valuable tool for computer modeling. . . . Any student who works through this text will develop a very good sense of what mathematical modeling is about. . . . This text would work well for self-study or as a source of material for projects." (Bill Satzer, MathDL - Online, April, 2006)

"All given algorithms have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. .... Moreover, each section of recipes is followed by a set of problems that reader can use to check their understanding. ... Therefore, this handbook is appropriate for any junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures." (Jerzy Martyna, Zentralblatt MATH, Vol. 1106 (8), 2007)

"The authors ... aim is to introduce the reader to what they call 'the 'new' computational science based on the utilization of a CAS [computer algebra system].' ... I ... enjoyed reading this book and I learned a lot of Maple as I went through the worksheets. ... a text in a course that equips undergraduates to analyze and solve problems with a CAS. ... the book might be described as a tutorial on Maple that is based on mathematical models." (L. F. Shampine, SIAM Review, Vol. 49 (1), 2007)