Introduction to Linear Algebra and Differential Equations

by John W. Dettman

Overview

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Product Details

ISBN-13:	9780486158310
Publisher:	Dover Publications
Publication date:	09/07/2012
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	432
File size:	20 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface
1. Complex Numbers
1.1 Introduction
1.2 The Algebra of Complex Numbers
1.3 The Geometry of Complex Numbers
1.4 Two-dimensional Vectors
1.5 Functions of a Complex Variable
1.6 Exponential Function
1.7 Power Series
2. Linear Algebraic Equations
2.1 Introduction
2.2 Matrices
2.3 Elimination Method
2.4 Determinants
2.5 Inverse of a Matrix
2.6 Existence and Uniqueness Theorems
3. Vector Spaces
3.1 Introduction
3.2 Three-dimensional Vectors
3.3 Axioms of a Vector Space
3.4 Dependence and Independence of Vectors
3.5 Basis and Dimension
3.6 Scalar Product
3.7 Orthonormal Bases
3.8 Infinite-dimensional Vector Spaces
4. Linear Transformations
4.1 Introduction
4.2 Definitions and Examples
4.3 Matrix Representations
4.4 Changes of Bases
4.5 Characteristic Values and Characteristic Vectors
4.6 Symmetric and Hermitian Matrices
4.7 Jordan Forms
5. First Order Differential Equations
5.1 Introduction
5.2 An Example
5.3 Basic Definitions
5.4 First Order Linear Equations
5.5 First Order Nonlinear Equations
5.6 Applications of First Order Equations
5.7 Numerical Methods
5.8 Existence and Uniqueness
6. Linear Differential Equations
6.1 Introduction
6.2 General Theorems
6.3 Variation of Parameters
6.4 Equations with Constant Coefficients
6.5 Method of Undetermined Coefficients
6.6 Applications
6.7 Green's Functions
7. Laplace Transforms
7.1 Introduction
7.2 Existence of the Transform
7.3 Transforms of Certain Functions
7.4 Inversion of the Transform
7.5 Solution of Differential Equations
7.6 Applications
7.7 Uniqueness of the Transform
8. Power-Series Methods
8.1 Introduction
8.2 Solution near Ordinary Points
8.3 Solution near Regular Singular Points
8.4 Bessel Functions
8.5 Boundary-value Problems
8.6 Convergence Theorems
9. Systems of Differential Equations
9.1 Introduction
9.2 First Order Systems
9.3 Linear First Order Systems
9.4 Linear First Order Systems with Constant Coefficients
9.5 Higher Order Linear Systems
9.6 Existence and Uniqueness Theorem
Answers and Hints for Selected Exercises; Index