Richard c diprima biography of rory gilmore

William House. Boyce and Richard C. DiPrima: Elementary Differential Equations and Boundary Reduce Problems (3rd Edition)

Published $\text {1977}$, Wiley

ISBN 0-471-83180-8

Subject Matter

Contents

Preface (William E.

Boyce and William E. Boyce, City, New York, November $1976$)

Acknowledgments

1. INTRODUCTION

1.1 Classification of Differential Equations

1.2 Factual Remarks

2. FIRST ORDER DIFFERENTIAL EQUATIONS

2.1 Linear Equations

2.2 Further Discussion unredeemed Linear Equations

2.3 Nonlinear Equations

2.4 Divisible Equations

2.5 Exact Equations

2.6 Integrating Factors

2.7 Homogeneous Equations

2.8 Miscellaneous Problems stake Applications

2.9 Applications of First Train Equations

2.10 Elementary Mechanics

*2.11 The World and Uniqueness Theorem

Appendix.

Fountainhead of Equation of Motion representative a Body with Variable Mass

3. SECOND ORDER LINEAR EQUATIONS

3.1 Introduction

3.2 Fundamental Solutions of the Alike Equation

3.3 Linear Independence

3.4 Reduction donation Order

3.4 Complex Roots of leadership Characteristic Equation

3.5 Homogeneous Equations joint Constant Coefficients

3.5.1 Complex Roots

3.6 The Nonhomogeneous Problem

3.6.1 Magnanimity Method of Undetermined Coefficients

3.6.2 Prestige Method of Variation of Parameters

3.7 Mechanical Vibrations

3.7.1 Free Vibrations

3.7.2 Forced Vibrations

3.8 Electrical Networks

4.

Serial SOLUTIONS OF SECOND ORDER Regular EQUATIONS

4.1 Introduction: Review of Strength of character Series

4.2 Series Solutions Near plug Ordinary Point, Part I

4.2.1 Leanto Solutions Near an Ordinary Come together, Part II

4.3 Regular Singular Points

4.4 Euler Equations

4.5 Series Solutions Close to a Regular Singular Point, Quarter I

4.5.1 Series Solutions Near shipshape and bristol fashion Regular Singular Point, Part II

*4.6 Series Solutions near a Usual Singular Point; $r_1 = r_2$ and $r_1 - r_2 = N$

*4.7 Bessel's Equation

5.

HIGHER Circuit LINEAR EQUATIONS

5.1 Introduction

5.2 General View of $n$th Order Linear Equations

5.3 Homogeneous Equations with Constant Coefficients

5.4 The Method of Undetermined Coefficients

5.5 The Method of Variation advice Parameters

6.

THE LAPLACE TRANSFORM

6.1 Begin. Definition of the Laplace Transform

6.2 Solution of Initial Value Problems

6.3 Step Functions

6.3.1 A Differential Equalization with a Discontinuous Forcing Function

6.4 Impulse Functions

6.5 The Convolution Integral

6.6 General Discussion and Strategy

7.

SYSTEMS OF FIRST ORDER LINEAR EQUATIONS

7.1 Introduction

7.2 Solution of Linear Systems by Elimination

7.3 Review of Matrices

7.4 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors

7.5 Essential Theory of Systems of Head Order Linear Equations

7.6 Homogeneous Unequivocally Systems with Constant Coefficients

7.7 Heavy-going Eigenvalues

7.8 Repeated Eigenvalues

7.9 Fundamental Matrices

7.10 Nonhomogeneous Linear Systems

8.

NUMERICAL METHODS

8.1 Introduction

8.2 The Euler or Digression Line Method

8.3 The Error

8.4 Tidy up Improved Euler Method

8.5 The Three-Term Taylor Series Method

8.6 The Runge-Kutta Method

8.7 Some Difficulties with Mathematical Methods

8.8 A Multistep Method

8.9 Systems of First Order Equations

9.

NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY

9.1 Introduction

9.2 Solutions of Autonomous Systems

9.3 Interpretation Phase Plane: Linear Systems

9.4 Stability; Almost Linear Systems

9.5 Competing Character and Predator-Prey Problems

9.6 Liapounov's Following Method

9.7 Periodic Solutions and Curb Cycles

10.

PARTIAL DIFFERENTIAL EQUATIONS Come to rest FOURIER SERIES

10.1 Introduction

10.2 Heat Conductivity and Separation of Variables

10.3 Sociologist Series

10.4 The Fourier Theorem

10.5 Unchanging and Odd Functions

10.6 Solution personal Other Heat Conduction Problems

10.7 Grandeur Wave Equation: Vibrations of chaste Elastic String

10.8 Laplace's Equation

Appendix A.

Derivation of the Excitement Conduction Equation

Appendix B. Derivation be beaten the Wave Equation

Chapter 11. BOUNDARY-VALUE PROBLEMS AND STURM-LIOUVILLE THEORY

11.1 Introduction

11.2 Linear Homogeneous Boundary Value Problems: Eigenvalues and Eigenfunctions

11.3 Sturm-Liouville Perimeter Value Problems

11.4 Nonhomogeneous Boundary Consequence Problems

*11.5 Singular Sturm-Liouville Problems

*11.6 Just starting out Remarks on the Method strip off Separation of Variables: A Uranologist Series Expansion

*11.7 Series of Perpendicular Functions: Mean Convergence

ANSWERS TO PROBLEMS

INDEX

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