Linear Algebra with Applications 9th Edition by Gareth Williams, ISBN-13: 978-1284120097
[PDF eBook eTextbook]
- Publisher: Jones & Bartlett Learning; 9th edition (December 15, 2017)
- Language: English
- 594 pages
- ISBN-10: 1284120090
- ISBN-13: 978-1284120097
Linear Algebra with Applications, Ninth Edition is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Updated to increase clarity and improve student learning, the author provides a flexible blend of theory and engaging applications. The material in Linear Algebra with Applications, Ninth Edition is arranged into three parts that contain core and optional sections: Part 1 introduces the basics, discussing systems of linear equations, vectors in Rn matrices, linear transformations, determinants, eigenvalues, and eigenspaces. Part 2 builds on this material to discuss general vector spaces, and includes such topics as the Rank-Nullity Theorem, inner products and coordinate representation. Part 3 completes the course with important ideas and methods in Numerical Linear Algebra including ill-conditioning, pivoting, LU decomposition and Singular Value Decomposition. Throughout the text the author provides interesting applications, ranging from theoretical applications such as the use of linear algebra in differential equations, to many practical applications in the fields of electrical engineering, traffic analysis, relativity, history, and more.
Table of Contents:
Title Page
Copyright
Dedication
Contents
Preface
PART 1 Linear Equations, Vectors, and Matrices
1 Linear Equations and Vectors
1.1 Matrices and Systems of Linear Equations
1.2 Gauss-Jordan Elimination
1.3 The Vector Space Rn
1.4 Subspaces of Rn
1.5 Basis and Dimension
1.6 Dot Product, Norm, Angle, and Distance (Option: This section can be deferred to just before Sect
1.7 Curve Fitting, Electrical Networks, and Traffic Flow
CHAPTER 1 REVIEW EXERCISES
2 Matrices and Linear Transformations
2.1 Addition, Scalar Multiplication, and Multiplication of Matrices
2.2 Properties of Matrix Operations
2.3 Symmetric Matrices and Seriation in Archaeology
2.4 The Inverse of a Matrix and Cryptography
2.5 Matrix Transformations, Rotations, and Dilations
2.6 Linear Transformations, Graphics, and Fractals
2.7 The Leontief Input-Output Model in Economics
2.8 Markov Chains, Population Movements, and Genetics
2.9 A Communication Model and Group Relationships in Sociology
CHAPTER 2 REVIEW EXERCISES
3 Determinants and Eigenvectors
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Determinants, Matrix Inverses, and Systems of Linear Equations
3.4 Eigenvalues and Eigenvectors (Option: Diagonalization of Matrices, Section 5.3, may be discussed
3.5 Google, Demography, Weather Prediction, and Leslie Matrix Models
CHAPTER 3 REVIEW EXERCISES
PART 2 Vector Spaces
4 General Vector Spaces
4.1 General Vector Spaces and Subspaces
4.2 Linear Combinations of Vectors
4.3 Linear Independence of Vectors
4.4 Properties of Bases
4.5 Rank
4.6 Projections, Gram-Schmidt Process, and QR Factorization
4.7 Orthogonal Complement
4.8 Kernel, Range, and the Rank/Nullity Theorem
4.9 One-to-One Transformations and Inverse Transformations
4.10 Transformations and Systems of Linear Equations
CHAPTER 4 REVIEW EXERCISES
5 Coordinate Representations
5.1 Coordinate Vectors
5.2 Matrix Representations of Linear Transformations
5.3 Diagonalization of Matrices
5.4 Quadratic Forms, Difference Equations, and Normal Modes
5.5 Linear Differential Equations (Calculus Prerequisite)
CHAPTER 5 REVIEW EXERCISES
6 Inner Product Spaces
6.1 Inner Product Spaces
6.2 Non-Euclidean Geometry and Special Relativity
6.3 Approximation of Functions and Coding Theory
6.4 Least Squares Solutions
CHAPTER 6 REVIEW EXERCISES
PART 3 Numerical Linear Algebra
7 Numerical Methods
7.1 Gaussian Elimination
7.2 The Method of LU Decomposition
7.3 Practical Difficulties in Solving Systems of Equations
7.4 Iterative Methods for Solving Systems of Linear Equations
7.5 Eigenvalues by Iteration and Connectivity of Networks
7.6 The Singular Value Decomposition
CHAPTER 7 REVIEW EXERCISES
8 Linear Programming
8.1 A Geometrical Introduction to Linear Programming
8.2 The Simplex Method
8.3 Geometrical Explanation of the Simplex Method
CHAPTER 8 REVIEW EXERCISES
Appendices
A Cross Product
B Equations of Planes and Lines in Three-Space
C Graphing Calculator Manual
C1 Reduced Echelon Form of a Matrix
C2 Matrix Operations
C3 Powers of a Matrix
C4 Transpose of a Matrix
C5 Inverse of a Matrix
C6 Determinant of a Matrix
C7 Summary of Formats for Row Operations
D MATLAB Manual
D1 Entering and Displaying a Matrix (Section 1.1)
D2 Solving Systems of Linear Equations (Sections 1.1, 1.2, 1.7)
D3 Dot Product, Norm, Angle, Distance (Section 1.6)
D4 Matrix Operations (Sections 2.1–2.3)
D5 Computational Considerations (Section 2.2)
D6 Inverse of a Matrix (Section 2.4)
D7 Solving Systems of Equations Using Matrix Inverse (Section 2.4)
D8 Cryptography (Section 2.4)
D9 Transformations Defined by Matrices (Sections 2.5, 2.6)
D10 Fractals (Section 2.6)
D11 Leontief I/O Model (Section 2.7)
D12 Markov Chains (Sections 2.8, 3.5)
D13 Digraphs (Section 2.9)
D14 Determinants (Sections 3.1—3.3)
D15 Cramer’s Rule (Section 3.3)
D16 Eigenvalues and Eigenvectors (Sections 3.4, 3.5)
D17 Linear Combinations, Dependence, Basis, Rank (Sections 1.3, 4.2–4.5)
D18 Projection, Gram-Schmidt Orthogonalization (Section 4.6)
D19 QR Factorization (Section 4.6)
D20 Kernel and Range (Section 4.8)
D21 Inner Product, Non-Euclidean Geometry (Sections 6.1, 6.2)
D22 Space–Time Travel (Section 6.2)
D23 Pseudoinverse and Least Squares Curves (Section 6.4)
D24 LU Decomposition (Section 7.2)
D25 Condition Number of a Matrix (Section 7.3)
D26 Jacobi and Gauss-Seidel Iterative Methods (Section 7.4)
D27 Singular Value Decomposition (Section 7.6)
D28 The Simplex Method in Linear Programming (Section 8.2)
D29 Cross Product (Appendix A)
D30 MATLAB Commands, Functions, and M-Files
D31 The Linear Algebra with Applications Toolbox M-Files
Answers to Selected Exercises
Index
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 has taught mathematics at the University of Florida, the University of Denver, and Stetson University. He has been an exchange professor at the 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. His publications include “Fine Topologies for Minkowski Space”, Motions in Relativistic Space”, “Mathematics in Archaeology”, and books on Finite Mathematics, Calculus, and College Algebra. He is the co-developer (with Lisa Coulter) of the linear algebra software package, “The Linear Algebra Toolbox” for MATLAB. Dr. Williams is a member of The Mathematics Association of America.
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