Linear Algebra with Applications 9th Edition by Gareth Williams – Ebook PDF Instant Download/Delivery: 1284120090, 9781284120097
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ISBN 10: 1284120090
ISBN 13: 9781284120097
Author: Gareth Williams
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. Features & Benefits • Updated to simplify earlier material in the text while going into later, more advanced material in more depth • Interesting applications, both theoretical and practical, engage and challenge students • Carefully explained and illustrated examples highlight key concepts through the text • A MATLAB manual, included as an appendix, consists of 31 sections that tie into course material • Available with WebAssign Online Homework and Assessment with integrated eBook Applicable Courses Written for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics.
Linear Algebra with Applications 9th Table of contents:
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
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