A Course in Ordinary and Partial Differential Equations

A Course in Ordinary and Partial Differential Equations

1st Edition - January 1, 1969

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  • Author: Zalman Rubinstein
  • eBook ISBN: 9781483262628

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Description

A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.

Table of Contents


  • Preface

    Part I. Ordinary Differential Equations

    Section 1 Classification and Solutions of First-Order Differential Equations

    1.1 General Remarks

    1.2 Solution of Elementary First-Order Differential Equations

    1.3 Integration Factors

    Section 2 Elementary Higher-Order Differential Equations

    Exercises

    Section 3 Existence Theorems

    Exercises

    Section 4 Singular Solutions

    Exercises

    Section 5 Linear Equations of Arbitrary Order

    Section 6 Solutions of Linear Equations

    6.1 Solution of Linear Equations with Constant Coefficients

    6.2 Operational Calculus and Solutions of Linear Differential Equations

    Exercises

    Section 7 Linear Systems with Constant Coefficients

    Exercises

    Section 8 Infinite Series Solutions

    Exercises

    Section 9 Asymptotic Expansion of Solutions of Linear Differential Equations

    Exercises

    Section 10 Solutions of Differential Equations by Definite Integrals

    Exercises

    Section 11 Boundary Value Problems

    11.1 Introduction

    Exercises

    11.2 Sturm-Liouville Systems

    Exercises

    Section 12 Green's Function

    Exercises

    Section 13 Expansion Theorems

    Exercises

    Section 14 Nonlinear Differential Equations

    14.1 General Remarks

    14.2 Autonomous Systems

    Exercises

    14.3 Stability of Solutions of Differential Equations

    Exercises

    Part II. Partial Differential Equations

    Section 1 Introduction

    Exercises

    Section 2 Elementary Second-Order Partial Differential Equations

    2.1 Classification of Second-Order Equations

    Exercises

    2.2 The Cauchy Problem and the Characteristic Surfaces

    Exercises

    Section 3 Second-Order Hyperbolic Differential Equations

    Exercises

    Section 4 Second-Order Elliptic Differential Equations

    Exercises

    Section 5 Second-Order Parabolic Differential Equations

    Exercises

    Section 6 The Fourier Transform and Its Applications to Partial Differential Equations

    6.1 Definition and Elementary Properties of the Fourier Transform

    6.2 Applications of the Fourier Transform to Elementary Differential Equations

    Exercises

    Section 7 Hilbert Space Approach to Partial Differential Equations

    Exercises

    Section 8 Distributions and Their Applications to Partial Differential Equations

    Exercises

    Index

Product details

  • No. of pages: 488
  • Language: English
  • Copyright: © Academic Press 1969
  • Published: January 1, 1969
  • Imprint: Academic Press
  • eBook ISBN: 9781483262628

About the Author

Zalman Rubinstein

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