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Computing with Maple

Author: Francis Wright

Publisher: CRC Press

Published: 2001-09-27

Total Pages: 558

ISBN-13: 9781584882367

Powerful, flexible, easy to use-small wonder that the use of MAPLE® continues to increase, particularly since the latest releases of MAPLE. The built-in nature of its numerical and graphical facilities gives MAPLE a distinct advantage over traditional programming languages, yet to date, no textbook has used that advantage to introduce programming concepts. Moreover, few books based on MAPLE's latest versions even exist. Computing with MAPLE presents general programming principles using MAPLE as a concrete example of a programming language. The author first addresses the basic MAPLE functions accessible for interactive use then moves to actual programming, discussing all of the programming facilities that MAPLE provides, including control structures, data types, graphics, spreadsheets, text processing, and object oriented programming. Reflecting MAPLE's primary function as a computational tool, the book's emphasis is on mathematical examples, and it includes a full chapter devoted to algebraic programming. Classroom tested since 1995, the material in Computing with MAPLE is particularly appropriate for an intermediate-level introductory course in programming for both mathematics and computing students. It includes numerous exercises and test questions, with MAPLE worksheets, contact information, and supplementary material available on the Internet.

Scientific Computing - An Introduction using Maple and MATLAB

Author: Walter Gander

Publisher: Springer Science & Business

Published: 2014-04-23

Total Pages: 905

ISBN-13: 3319043250

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Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Mathematical Computing

Author: David Betounes

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 412

ISBN-13: 1461300673

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This book teaches introductory computer programming using Maple, offering more mathematically oriented exercises and problems than those found in traditional programming courses, while reinforcing and applying concepts and techniques of calculus. Includes case studies.

Solving Problems in Scientific Computing Using Maple and Matlab®

Author: Walter Gander

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 268

ISBN-13: 364297533X

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Modern computing tools like Maple (symbolic computation) and Matlab (a numeric computation and visualization program) make it possible to easily solve realistic nontrivial problems in scientific computing. In education, traditionally, complicated problems were avoided, since the amount of work for obtaining the solutions was not feasible for the students. This situation has changed now, and the students can be taught real-life problems that they can actually solve using the new powerful software. The reader will improve his knowledge through learning by examples and he will learn how both systems, MATLAB and MAPLE, may be used to solve problems interactively in an elegant way. Readers will learn to solve similar problems by understanding and applying the techniques presented in the book. All programs used in the book are available to the reader in electronic form.

An Introduction to Modern Mathematical Computing

Author: Jonathan M. Borwein

Publisher: Springer Science & Business Media

Published: 2012-08-07

Total Pages: 237

ISBN-13: 1461442532

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Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

Maple and Mathematica

Author: Inna K. Shingareva

Publisher: Springer Science & Business Media

Published: 2009-08-14

Total Pages: 500

ISBN-13: 3211994327

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In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.

Experimental Mathematics with Maple

Author: Franco Vivaldi

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 151

ISBN-13: 1351990195

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As discrete mathematics rapidly becomes a required element of undergraduate mathematics programs, algebraic software systems replace compiled languages and are now most often the computational tool of choice. Newcomers to university level mathematics, therefore, must not only grasp the fundamentals of discrete mathematics, they must also learn to use an algebraic manipulator and develop skills in abstract reasoning. Experimental Mathematics with MAPLE uniquely responds to these needs. Following an emerging trend in research, it places abstraction and axiomatization at the end of a learning process that begins with computer experimentation. It introduces the foundations of discrete mathematics and, assuming no previous knowledge of computing, gradually develops basic computational skills using the latest version of the powerful MAPLE® software. The author's approach is to expose readers to a large number of concrete computational examples and encourage them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. Using this approach, Experimental Mathematics with MAPLE enables readers to build a foundation in discrete mathematics, gain valuable experience with algebraic computing, and develop a familiarity with basic abstract concepts, notation, and jargon. Its engaging style, numerous exercises and examples, and Internet posting of selected solutions and MAPLE worksheets make this text ideal for use both in the classroom and for self-study.

Introduction to the Tools of Scientific Computing

Author: Einar Smith

Publisher: Springer Nature

Published: 2020-12-02

Total Pages: 344

ISBN-13: 3030608085

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The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing. The fact that different languages are studied and compared also makes the book useful for mathematicians and practitioners trying to decide which programming language to use for which purposes.