Ordinary and partial differential equations /
Henner, Victor.
Belozerova, Tatyana.
Khenner, Mikhail.
"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. 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. Requiring no user programming, the accompanying computer software allows readers 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."-- P. 4 of cover.
"An A K Peters book."
Includes bibliographical references and index.
Ch. 1. First-order differential equations -- Ch. 2. Second-order differential equations -- Ch. 3. Systems of differential equations -- Ch. 4. Boundary value problems for second-order ODE and Sturm-Liouville theory -- Ch. 5. Qualitative methods and stability of ODE solutions -- Ch. 6. Method of Laplace transforms for ODE -- Ch. 7. Integral equations -- Ch. 8. Series solutions of ODE and Bessel and Legendre equations -- Ch. 9. Fourier series -- Ch. 10. One-dimensional hyperbolic equations -- Ch. 11. Two-dimensional hyperbolic equations -- Ch. 12. One-dimensional parabolic equations -- Ch. 13. Two-dimensional parabolic equations -- Ch. 14. 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 section 5.25 -- Appendix 5. How to use the software associated with the book.
"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. 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. Requiring no user programming, the accompanying computer software allows readers 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."-- P. 4 of cover.
Differential equations
Differential equations, Partial
MATHEMATICS / Advanced.
MATHEMATICS / Applied.
MATHEMATICS / Differential Equations.