http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Linear Methods: A General Education Course is expressly written for non-mathematical students, particularly freshmen taking a required core mathematics course. Rather than covering a hodgepodge of different topics as is typical for a core mathematics course, this text encourages students to explore one particular branch of mathematics, elementary linear algebra, in some depth. The material is presented in an accessible manner, as opposed to a traditional overly rigorous approach. While introducing students to useful topics in linear algebra, the book also includes a gentle introduction to more abstract facets of the subject.
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface for the Instructor; Preface for the Student; 1 Matrices; 1.1 Introduction to Matrices; 1.2 Matrix Addition and Scalar Multiplication; 1.3 Fundamental Properties of Addition and Scalar Multiplication; 1.4 Transpose of a Matrix; 1.5 Special Matrices; 1.6 Matrix Multiplication; 1.7 Algebraic Rules for Matrix Multiplication; 1.8 Matrix Multiplication and Linear Combinations; 1.9 Chapter 1 Test; 2 Application: Elementary Graph Theory; 2.1 Graphs and Digraphs: Definitions; 2.2 The Adjacency Matrix.
2.3 Counting Paths and Connectivity2.4 Chapter 2 Test; 3 Vectors; 3.1 Vector Fundamentals; 3.2 Vector Operations and Geometry; 3.3 The Dot Product of Vectors; 3.4 The Angle Between Vectors; 3.5 Projection Vectors; 3.6 Linear Combinations with Mutually Orthogonal Vectors; 3.7 Chapter 3 Test; 4 Solving Systems of Linear Equations; 4.1 Systems of Linear Equations; 4.2 Row Operations on Augmented Matrices; 4.3 Introduction to Gauss-Jordan Row Reduction; 4.4 The Remaining Cases of the Gauss-Jordan Method; 4.5 Reduced Row Echelon Form and Rank of a Matrix.
4.6 Homogeneous Systems and Mutually Orthogonal Sets4.7 Chapter 4 Test; 5 Application: Least-Squares; 5.1 Approximation by a Linear Function; 5.2 Higher Degree Polynomials; 5.3 How Does Least-Squares Work?; 5.4 Chapter 5 Test; 6 Inverses for Matrices; 6.1 Multiplicative Inverses; 6.2 Properties of Inverse Matrices; 6.3 Orthogonal Matrices and Mutually Orthogonal Sets; 6.4 Chapter 6 Test; 7 Geometric Transformations with Matrices; 7.1 Matrix Transformations of the Plane; 7.2 Compositions and Inverses of Transformations; 7.3 Homogeneous Coordinates; 7.4 Chapter 7 Test.
A Answers to Odd-Numbered ExercisesB Properties, Theorems, and Methods; Index.
Includes bibliographical references and index.
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