Linear Algebra with Applications

Gareth Williams

666 pages, parution le 01/01/2001 (4^eme édition)

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Résumé

Linear Algebra with Applications is a flexible blend of theory, important computational techniques, and interesting applications. Instructors can select the topics that give the course their desired perspective. The text provides a solid foundation in the mathematics of linear algebra, while introducing some of the important computational aspects of the field, such as algorithms. The presentation of interesting applications has been one of the most compelling features of this book provides students a well balanced coverage of standard linear algebra topics that apply mathematics by examining real-life applications, making for a enlightening learning experience.

Features

New to this Edition! Introduction to Elimination Methods: An improved introduction of the Gauss-Jordan method is given.
New to this Edition! Chapter on Vector Space Rn contains an introduction to dot product, angle, magnitude, distance, and an early introduction to linear transformations with applications in computer graphics and fractals.
New to this Edition! Eigenvalues and Eigenvectors: used in discussing long term trends of phenomena and the diagonalization of matrices are discussed.
New to this Edition! MATLAB and Graphing Calculator: Collected into manuals at the end of the book, positioned for easy reference.
The concepts of linear combinations of vectors, linear dependence, and dimension are introduced within the context of general vector spaces.
The best collection of applications of any linear algebra text, range from theoretical applications, such as, differential equations to practical applications, such as, archaeology and demography.

Contents

Chapter 1 Systems of Linear Equations

Matrices and Systems of Linear Equations
Gauss-Jordan Elimination
Curve Fitting, Electrical Networks, and Traffic Flow
Chapter 1 Review Exercises

Chapter 2 Matrices

Addition, Scalar Multiplication, and Multiplication of Matrices
Properties of Matrix Operations
Symmetric Matrices and Seriation in Archaeology
The Inverse of a Matrix and Cryptography
The Leontief Input-Output Model in Economics
Markov Chains, Population Movements, and Genetics
A Communication Model and Group Relationships in Sociology
Chapter 2 Review Exercises

Chapter 3 Determinants

Introduction to Determinants
Properties of Determinants
Numerical Evaluation of a Determinant
Determinants, Matrix Inverses, and Systems of Linear Equations
Chapter 3 Review Exercises

Chapter 4 The Vector Space Rn

Introduction to Vectors
Dot Product, Norm, Angle, and Distance
Introduction to Linear Transformations
Matrix Transformations, Computer Graphics, and Fractals
Chapter 4 Review Exercises

Chapter 5 General Vector Spaces

Vector Spaces
Subspaces
Linear Combinations of Vectors
Linear Dependence and Independence
Bases and Dimension
Rank of a Matrix
Orthonormal Vectors and Projections in Rn
Chapter 5 Review Exercises

Chapter 6 Eigenvalues and Eigenvectors

Eigenvalues, Eigenvectors, and Eigenspaces
Demography and Weather Prediction
Diagonalization of Matrices
Quadratic Forms, Difference Equations, and Normal Modes
Chapter 6 Review Exercises

Chapter 7 Linear Transformations

Linear Transformations, Kernel, and Range
Transformations and Systems of Linear Equations
Coordinate Vectors
Matrix Representations of Linear Transformations
Chapter 7 Review Exercises

Chapter 8 Inner Product Spaces

Inner Product Spaces
Non-Euclidean Geometry and Special Relativity
Approximation of Functions and Coding Theory
Least=Squares Curves
Chapter 8 Review Exercises

Chapter 9 Numerical Techniques

Gaussian Elimination
The Method of LU Decomposition
Practical Difficulties in Solving Systems of Equations
Iterative Methods for Solving Systems of Linear Equations
Eigenvalues by Iteration and Connectivity of Networks
Chapter 9 Review Exercises

Chapter 10 Linear Programming

A Geometrical Introduction to Linear Programming
The Simplex Method
Geometrical Explanation of the Simplex Method
Chapter 10 Review Exercises

Appendices

A Cross Product
B Equations of Lines in Three-Space
C Graphing Calculator Manual
D MATLAB Manual

L'auteur - Gareth Williams

Gareth Williams earned a B.S. and a Ph.D. in applied mathematics from the University of Wales, and did graduate work at Kings College University of London. He was formerly on the faculties of the University of Florida and the University of Denver, and now teaches math at Stetson University. He has been an exchange professor at Paedagogische Hochschule, in Freiburg, Germany and has spent sabbaticals at the University of Wales. His mathematical interests include linear algebra, relativity, mathematical modeling, and the computer in mathematics education. Other publications include "The Microcomputer in Linear Algebra", "Fine Topologies for Minkowski Space", "Mathematics in Archaeology", and books on Finite Mathematics, Calculus, and College Algebra. He is the developer of the linear algebra software, "The Linear Algebra Toolbox", for MATLAB, and Mathematica notebooks. Williams is a member of Mathematics Association of America, the American Mathematical Society, and The International Linear Algebra Society. For relaxation Dr. Williams plays golf and tennis and likes to travel.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Jones and Bartlett Computer Science
Auteur(s)	Gareth Williams
Parution	01/01/2001
Édition	4^eme édition
Nb. de pages	666
Format	19,5 x 24
Couverture	Relié
Poids	1308g
Intérieur	2 couleurs
EAN13	9780763714512
ISBN13	978-0-7637-1451-2