Elementary Differential Equations with Linear Algebra - 3rd Edition - ISBN: 9780125739450, 9781483262376

Elementary Differential Equations with Linear Algebra

3rd Edition

Authors: Albert L. Rabenstein
eBook ISBN: 9781483262376
Imprint: Academic Press
Published Date: 1st January 1982
Page Count: 528
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Description

Elementary Differential Equations with Linear Algebra, Third Edition provides an introduction to differential equation and linear algebra. This book includes topics on numerical methods and Laplace transforms. Organized into nine chapters, this edition begins with an overview of an equation that involves a single unknown function of a single variable and some finite number of its derivatives. This text then examines a linear system of two equations with two unknowns. Other chapters consider a class of linear transformations that are defined on spaces of functions wherein these transformations are essential in the study of linear differential equations. This book discusses as well the linear differential equations whose coefficients are constant functions. The final chapter deals with the properties of Laplace transform in detail and examine as well the applications of Laplace transforms to differential equations. This book is a valuable resource for mathematicians, students, and research workers.

Table of Contents


Preface

One Introduction to Differential Equations

1.1 Introduction

1.2 Separable Equations

1.3 Exact Equations

1.4 First-Order Linear Equations

1.5 Orthogonal Trajectories

1.6 Radioactive Decay

1.7 Mixing Problems

1.8 Population Growth

1.9 Economic Models

1.10 Cooling; The Rate of a Chemical Reaction

1.11 Two Special Types of Second-Order Equations

1.12 Falling Bodies

1.13 Some Theoretical Matters

Two Matrices and Determinants

2.1 Systems of Linear Equations

2.2 Homogeneous Systems

2.3 Applications Involving Systems of Equations

2.4 Matrices and Vectors

2.5 Matrix Multiplication

2.6 Inner Product and Length

2.7 Some Special Matrices

2.8 Determinants

2.9 Properties of Determinants

2.10 Cofactors

2.11 Cramer's Rule

2.12 The Inverse of a Matrix

Three Vector Spaces and Linear Transformations

3.1 Vector Spaces

3.2 Subspaces

3.3 Linear Dependence

3.4 Wronskians

3.5 Dimension

3.6 Orthogonal Bases

3.7 Linear Transformations

3.8 Properties of Linear Transformations

3.9 Differential Operators

Four Characteristic Values

4.1 Characteristic Values

4.2 An Application: Population Growth

4.3 Diagonalization

4.4 Real Symmetric Matrices

4.5 Functions of Matrices

Five Linear Differential Equations

5.1 Introduction

5.2 Polynomial Operators

5.3 Complex Solutions

5.4 Equations with Constant Coefficients

5.5 Cauchy-Euler Equations

Details

No. of pages:
528
Language:
English
Copyright:
© Academic Press 1982
Published:
Imprint:
Academic Press
eBook ISBN:
9781483262376

About the Author

Albert L. Rabenstein

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