Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations

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Features

    • Provides full coverage of ODEs and PDEs for students in the physical, engineering, biological, and mathematical sciences
    • Uses a teaching-by-examples philosophy—including extensive examples and exercises
    • Offers user-friendly software (with tutorials, GUI, and solution visualization capability) for the analytical solution and investigation of PDEs and ODEs
    • Presents advanced topics on ODEs and PDEs

    Figure slides and solutions manual available with qualifying course adoption

    Summary

    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

    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

    Editorial 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

     
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