Ordinary and Partial Differential Equations: 1st Edition (Paperback) book cover

Ordinary and Partial Differential Equations

1st Edition

By Victor Henner, Tatyana Belozerova, Mikhail Khenner

A K Peters/CRC Press

644 pages

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Description

Covers ODEs and PDEs—in One Textbook

Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software.



Teaches the Key Topics in Differential Equations

The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques.



Guides Students through the Problem-Solving Process

Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.

Table of Contents

First-Order Differential Equations. Second-Order Differential Equations. Systems of Differential Equations. Boundary Value Problems for Second-Order ODE and Sturm-Liouville Theory. Qualitative Methods and Stability of ODE Solutions. Method of Laplace Transforms for ODE. Integral Equations. Series Solutions of ODEs and Bessel and Legendre Equations. Fourier Series. Introduction to PDE. One-Dimensional Hyperbolic Equations. Two-Dimensional Hyperbolic Equations. One-Dimensional Parabolic Equations. Two-Dimensional Parabolic Equations. Elliptic Equations. Appendices. Bibliography.

About the Authors

Henner, Victor; Belozerova, Tatyana; Khenner, Mikhail

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT004000
MATHEMATICS / Arithmetic
MAT007000
MATHEMATICS / Differential Equations