Shiskowski, Frinkle

Linear Algebra with Mathematic

• Gebundenes Buch

Produktbeschreibung

Principles of Linear Algebra with Mathematica(r) uniquely addresses the quickly growing intersection between subject theory and numerical computation. Computer algebra systems such as Mathematica(r) are becoming ever more powerful, useful, user friendly and readily available to the average student and professional, but thre are few books which currently cross this gap between linear algebra and Mathematica(r). This book introduces algebra topics which can only be taught with the help of computer algebra systems, and the authors include all of the commands required to solve complex and computationally challenging linear algebra problems using Mathematica(r). The book begins with an introduction to the commands and programming guidelines for working with Mathematica(r). Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, vector projection, are explored as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear programming, linear transformations from Rn to Rm, the geometry of linear and affine transformations, and least squares fits and pseudoinverses. Although computational in nature, the material is not presented in a simply theory-proof-problem format. Instead, all topics are explored in a reader-friendly and insightful way. The Mathematica(r) software is fully utilized to highlight the visual nature of the topic, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. Exercises are supplied in most chapters, and a related Web site houses Mathematica(r) code so readers can work through the provided examples.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 624
• Erscheinungstermin: 13. Juni 2011
• Englisch
• Abmessung: 240mm x 161mm x 38mm
• Gewicht: 1094g
• ISBN-13: 9780470637951
• ISBN-10: 0470637951
• Artikelnr.: 33122732

Autorenporträt

Kenneth Shiskowski, PhD, is Professor of Mathematics at Eastern Michigan University. His areas of research interest include numerical analysis, history of mathematics, the integration of technology into mathematics, differential geometry, and dynamical systems. Dr. Shiskowski is the coauthor of Principles of Linear Algebra with Maple, published by Wiley. Karl Frinkle, PhD, is Associate Professor of Mathematics at Southeastern Oklahoma State University. His areas of research include Bose-Einstein condensates, nonlinear optics, dynamical systems, and integrating technology into mathematics. Dr. Frinkle is the coauthor of Principles of Linear Algebra with Maple, published by Wiley.

Inhaltsangabe

Preface. Conventions and Notations. 1. An Introduction to Mathematica. 1.1
The Very Basics. 1.2 Basic Arithmetic. 1.3 Lists and Matrices. 1.4
Expressions Versus Functions. 1.5 Plotting and Animations. 1.6 Solving
Systems of Equations. 1.7 Basic Programming. 2. Linear Systems of Equations
and Matrices. 2.1 Linear Systems of Equations. 2.2 Augmented Matrix of a
Linear System and Row Operations. 2.3 Some Matrix Arithmetic. 3.
Gauss-Jordan Elimination and Reduced Row Echelon Form. 3.1 Gauss-Jordan
Elimination and rref. 3.2 Elementary Matrices. 3.3 Sensitivity of Solutions
to Error in the Linear System. 4. Applications of Linear Systems and
Matrices. 4.1 Applications of Linear Systems to Geometry. 4.2 Applications
of Linear Systems to Curve Fitting. 4.3 Applications of Linear Systems to
Economics. 4.4 Applications of Matrix Multiplication to Geometry. 4.5 An
Application of Matrix Multiplication to Economics. 5. Determinants,
Inverses, and Cramer' Rule. 5.1 Determinants and Inverses from the Adjoint
Formula. 5.2 Determinants by Expanding Along Any Row or Column. 5.3
Determinants Found by Triangularizing Matrices. 5.4 LU Factorization. 5.5
Inverses from rref. 5.6 Cramer's Rule. 6. Basic Linear Algebra Topics. 6.1
Vectors. 6.2 Dot Product. 6.3 Cross Product. 6.4 A Vector Projection. 7. A
Few Advanced Linear Algebra Topics. 7.1 Rotations in Space. 7.2 "Rolling" a
Circle Along a Curve. 7.3 The TNB Frame. 8. Independence, Basis, and
Dimension for Subspaces of Rn. 8.1 Subspaces of Rn. 8.2 Independent and
Dependent Sets of Vectors in Rn. 8.3 Basis and Dimension for Subspaces of
Rn. 8.4 Vector Projection onto a subspace of Rn. 8.5 The Gram-Schmidt
Orthonormalization Process. 9. Linear Maps from Rn to Rm. 9.1 Basics About
Linear Maps. 9.2 The Kernel and Image Subspaces of a Linear Map. 9.3
Composites of Two Linear Maps and Inverses. 9.4 Change of Bases for the
Matrix Representation of a Linear Map. 10. The Geometry of Linear and
Affine Maps. 10.1 The Effect of a Linear Map on Area and Arclength in Two
Dimensions. 10.2 The Decomposition of Linear Maps into Rotations,
Reflections, and Rescalings in R2. 10.3 The Effect of Linear Maps on
Volume, Area, and Arclength in R3. 10.4 Rotations, Reflections, and
Rescalings in Three Dimensions. 10.5 Affine Maps. 11. Least-Squares Fits
and Pseudoinverses. 11.1 Pseudoinverse to a Nonsquare Matrix and Almost
Solving an Overdetermined Linear System. 11.2 Fits and Pseudoinverses. 11.3
Least-Squares Fits and Pseudoinverses. 12. Eigenvalues and Eigenvectors.
12.1 What Are Eigenvalues and Eigenvectors, and Why Do We Need Them? 12.2
Summary of Definitions and Methods for Computing Eigenvalues and
Eigenvectors as well as the Exponential of a Matrix. 12.3 Applications of
the Diagonalizability of Square Matrices. 12.4 Solving a Square First-Order
Linear System if Differential Equations. 12.5 Basic Facts About
Eigenvalues, Eigenvectors, and Diagonalizability. 12.6 The Geometry of the
Ellipse Using Eigenvalues and Eigenvectors. 12.7 A Mathematica
EigenFunction. Suggested Reading. Indices. Keyword Index. Index of
Mathematica Commands.

Rezensionen

"An accessible introduction to the theoretical and computational aspects of linear algebra using Maple(TM)." (TMCnet.com, 16 April 2011)