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1st Edition - January 1, 1969

Author: Zalman Rubinstein

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 6 2 6 2 - 8

A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary… Read more

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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.

PrefacePart 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 ExercisesPart 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 ExercisesIndex

- No. of pages: 488
- Language: English
- Edition: 1
- Published: January 1, 1969
- Imprint: Academic Press
- eBook ISBN: 9781483262628

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