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Matrix Vector Analysis

By: RICHARD L. EISENMAN

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Paperback | 24 March 2005

At a Glance

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320 Pages

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20.9 x 13.6 x 1.91

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This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.
Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structure. A combination of matrix and vector methods reinforces both techniques. "Applied" students learn that general theory is a natural and useful culmination of their computations, and "pure" students learn that concrete problems from the physical world have traditionally keynoted abstract intellectual pursuits.
Geared toward upper-level undergraduates, the text features approximately 50 provocative problems at each chapter's end that test students' choice of techniques. Each chapter is also followed by about 25 mental exercises that stimulate imaginative reflection. Answers are given to selected questions.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Calculus & Mathematical Analysis

Preface	p. iii
Static Vectors in 3-space	p. 1
Vectors and Equality	p. 1
Vector Sum and Vector Product	p. 3
Scalar Multiplication and Linear Dependence	p. 9
Projection and Inner Product	p. 14
Mixed Operations	p. 18
Basis	p. 24
Change of Basis via Matrices	p. 29
Functions of One Variable	p. 46
Derivative in a Fixed Basis	p. 46
Velocity and Acceleration	p. 50
Space-curve Geometry	p. 56
Relative Derivatives	p. 64
Rotation and Coriolis	p. 69
Vector and Scalar Fields	p. 85
Point Functions	p. 85
Derivatives of a Scalar Point Function	p. 90
Derivatives of a Vector Point Function	p. 98
Laplacian and Other Second [down triangle, open] Derivatives	p. 103
Vector Notation in Scalar Integrals	p. 109
Line Integrals	p. 112
Surface and Volume Integrals	p. 116
Integral Transformation Theorems	p. 122
Coordinate Systems	p. 153
Selecting Coordinates	p. 153
Selecting Basis Vectors	p. 159
Vector Algebra in a New System	p. 164
Del Operations in a New System	p. 169
Applications of Matrices	p. 185
Coding Messages	p. 185
Coding Algebraic Equations	p. 189
Linear Transformations	p. 198
Eigenproblems	p. 204
Linear Differential Equations	p. 211
Quadratic Forms	p. 218
Markov Chains	p. 226
Summary	p. 235
Practical Abstractions	p. 247
Abstract and Applied Elements	p. 247
Groups	p. 249
Function Spaces	p. 259
Finite-dimensional Vector Spaces	p. 269
Index	p. 307
Table of Contents provided by Ingram. All Rights Reserved.

Matrix Vector Analysis

At a Glance

Paperback

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