Ordinary and Partial Differential Equations
A K Peters/CRC Press – 2013 – 644 pages
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.
"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
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
Series Solutions of ODEs and Bessel and Legendre Equations
Partial Differential Equations
Introduction to PDE
One-Dimensional Hyperbolic Equations
Two-Dimensional Hyperbolic Equations
One-Dimensional Parabolic Equations
Two-Dimensional Parabolic 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