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Ordinary and Partial Differential Equations

By Victor Henner, Tatyana Belozerova, Mikhail Khenner

A K Peters/CRC Press – 2013 – 644 pages

Purchasing Options:

  • Add to CartHardback: $89.95
    978-1-46-651500-0
    January 28th 2013

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.

Reviews

"Ordinary and Partial Differential Equations provides college-level readers with a comprehensive textbook covering both ordinary differential equations and partial differential equations, offering a complete course on both under one cover, which makes this a unique contribution to the field. Examples and exercises accompany software supporting these and a text that covers all the basics any undergraduate or beginning graduate course will cover in differential equations. This doesn't require programmer knowledge nor any special computer software outside the disc provided here, and provides in-depth detail for students in the physical, engineering, biological, and math sciences using examples throughout. Very highly recommended for any college collection supporting these disciplines."

Midwest Book Review

"Henner, Belozerova, and Khenner cover most of the fundamental topics found in introductory ODEs and PDEs courses, nicely balancing scope without sacrificing content. … The authors have managed to provide the right amount of details and have outlined the text in such a way that all material needed to solve the PDEs discussed in Part II can be referenced within the text. This, in my opinion, is the main strength of the book. … this single book could be used successfully for a series of differential equations courses that covered both ODEs and PDEs if the same students took the courses. … This text finds a nice balance between general topics of ODEs and second-order PDEs."

—Joe Latulippe, MAA Reviews, June 2013

Contents

Ordinary Differential Equations, Boundary Value Problems, Fourier Series, and the Introduction to Integral Equations

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

Partial Differential Equations

Introduction to PDE

One-Dimensional Hyperbolic Equations

Two-Dimensional Hyperbolic Equations

One-Dimensional Parabolic Equations

Two-Dimensional Parabolic Equations

Elliptic Equations

Appendix 1: Eigenvalues and Eigenfunctions of One-Dimensional Sturm-Liouville Boundary Value Problem for Different Types of Boundary Conditions

Appendix 2: Auxiliary Functions, w(x,t), for Different Types of Boundary Conditions

Appendix 3: Eigenfunctions of Sturm-Liouville Boundary Value Problem for the Laplace Equation in a Rectangular Domain for Different Types of Boundary Conditions

Appendix 4: A Primer on the Matrix Eigenvalue Problems and the Solution of the Selected Examples in Sec. 5.2

Appendix 5: How to Use the Software Associated with the Book

Bibliography

Name: Ordinary and Partial Differential Equations (Hardback)A K Peters/CRC Press 
Description: By Victor Henner, Tatyana Belozerova, Mikhail Khenner. Covers ODEs and PDEs—in One TextbookUntil now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial...
Categories: Applied Mathematics, Differential Equations, Mathematical Physics