Elementary Linear Algebra with CD-ROM / Edition 5

by Larson, Bruce H Edwards, Ron Larson

Overview

The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.

Product Details

ISBN-13:	9780618400508
Publisher:	Houghton Mifflin Company College Division
Publication date:	07/28/2003
Edition description:	5TH BK&CDR
Pages:	544
Product dimensions:	8.26(w) x 9.44(h) x 0.92(d)

About the Author

Ron Larson received his PhD. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His Interactive Calculus (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and it was the first mainstream college textbook to be offered on the Internet.

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.

Table of Contents

Contents

Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects.

What Is Linear Algebra?
1. Systems of Linear Equations
Biographical Sketch of Carl Friedrich Gauss
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination and Gauss-Jordan Elimination
1.3 Applications of Systems of Linear Equations
2. Matrices
Biographical Sketch of Arthur Cayley
2.1 Operations with Matrices
2.2 Properties of Matrix Operations
2.3 The Inverse of a Matrix
2.4 Elementary Matrices
2.5 Applications of Matrix Operations
3. Determinants
Biographical Sketch of Augustin-Louis Cauchy
3.1 The Determinant of a Matrix
3.2 Evaluation of a Determinant Using Elementary Operations
3.3 Properties of Determinants
3.4 Introduction to Eigenvalues
3.5 Applications of Determinants
Cumulative Test for Chapters 1–3
4. Vector Spaces
Biographical Sketch of William Rowan Hamilton
4.1 Vectors in Rn
4.2 Vector Spaces
4.3 Subspaces of Vector Spaces
4.4 Spanning Sets and Linear Independence
4.5 Basis and Dimension
4.6 Rank of a Matrix and Systems of Linear Equations
4.7 Coordinates and Change of Basis
4.8 Applications of Vector Spaces
5. Inner Product Spaces
Biographical Sketch of Jean-Baptiste Joseph Fourier
5.1 Length and Dot Product in Rn
5.2 Inner Product Spaces
5.3 Orthonormal Bases: Gram-Schmidt Process
5.4 Mathematical Models and Least Squares Analysis
5.5 Applications of Inner Product Spaces
Cumulative Test for Chapters 4 and 5
6. Linear Transformations
Biographical Sketch of Emmy Noether
6.1Introduction to Linear Transformations
6.2 The Kernel and Range of a Linear Transformation
6.3 Matrices for Linear Transformations
6.4 Transition Matrices and Similarity
6.5 Applications of Linear Transformations
7. Eigenvalues and Eigenvectors
Biographical Sketch of James Joseph Sylvester
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
7.3 Symmetric Matrices and Orthogonal Diagonalization
7.4 Applications of Eigenvalues and Eigenvectors
Cumulative Test for Chapters 6 and 7
8. Complex Vector Spaces*
Biographical Sketch of Charles Hermite
8.1 Complex Numbers
8.2 Conjugates and Division of Complex Numbers
8.3 Polar Form and DeMoivre's Theorem
8.4 Complex Vector Spaces and Inner Products
8.5 Unitary and Hermitian Matrices
9. Linear Programming*
Biographical Sketch of John von Neumann
9.1 Systems of Linear Inequalities
9.2 Linear Programming Involving Two Variables
9.3 The Simplex Method: Maximization
9.4 The Simplex Method: Minimization
9.5 The Simplex Method: Mixed Constraints
10. Numerical Methods*
Biographical Sketch of Carl Gustav Jacob Jacobi
10.1 Gaussian Elimination with Partial Pivoting
10.2 Interative Methods for Solving Linear Systems
10.3 Power Method for Approximating Eigenvalues
10.4 Applications of Numerical Methods
Appendices
A. Mathematical Induction and Other Forms of Proofs
B. Computer Algebra Systems and Graphing Calculators
Answer Key
Index
* Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site.