Principles Of Linear Algebra With Mathematica

Author: Kenneth M. Shiskowski
Editor: John Wiley & Sons
ISBN: 1118627261
Size: 17,76 MB
Format: PDF

A hands-on introduction to the theoretical and computationalaspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationallyintensive, and computer algebra systems such as Mathematica®are essential not only for learning to apply the concepts tocomputationally challenging problems, but also for visualizing manyof the geometric aspects within this field of study. Principles ofLinear Algebra with Mathematica uniquely bridges the gap betweenbeginning linear algebra and computational linear algebra that isoften encountered in applied settings, and the commands required tosolve complex and computationally challenging problems usingMathematica are provided. The book begins with an introduction to the commands andprogramming guidelines for working with Mathematica. Next, theauthors explore linear systems of equations and matrices,applications of linear systems and matrices, determinants,inverses, and Cramer's rule. Basic linear algebra topics, such asvectors, dot product, cross product, and vector projection areexplored, as well as a unique variety of more advanced topicsincluding rotations in space, 'rolling' a circle along a curve, andthe TNB Frame. Subsequent chapters feature coverage of lineartransformations from Rn to Rm, the geometry of linear and affinetransformations, with an exploration of their effect on arclength,area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlesslyintegrated throughout the book through symbolic manipulations,numerical computations, graphics in two and three dimensions,animations, and programming. Each section concludes with standardproblems in addition to problems that were specifically designed tobe solved with Mathematica, allowing readers to test theircomprehension of the presented material. All related Mathematicacode is available on a corresponding website, along with solutionsto problems and additional topical resources. Extensively class-tested to ensure an accessible presentation,Principles of Linear Algebra with Mathematica is an excellent bookfor courses on linear algebra at the undergraduate level. The bookis also an ideal reference for students and professionals who wouldlike to gain a further understanding of the use of Mathematica tosolve linear algebra problems.

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