Ordinary and Partial Differential Equations

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