Ordinary and Partial Differential Equations

• Solvable Differential Equations.- Second-Order Differential Equations.- Preliminaries to Series Solutions.- Solution at an Ordinary Point.- Solution at a Singular Point.- Solution at a Singular Point (Cont’d.).- Legendre Polynomials and Functions.- Chebyshev, Hermite and Laguerre Polynomials.- Bessel Functions.- Hypergeometric Functions.- Piecewise Continuous and Periodic Functions.- Orthogonal Functions and Polynomials.- Orthogonal Functions and Polynomials (Cont’d.).- Boundary Value Problems.- Boundary Value Problems (Cont’d.).- Green’s Functions.- Regular Perturbations.- Singular Perturbations.- Sturm–Liouville Problems.- Eigenfunction Expansions.- Eigenfunction Expansions (Cont’d.).- Convergence of the Fourier Series.- Convergence of the Fourier Series (Cont’d.).- Fourier Series Solutions of Ordinary Differential Equations.- Partial Differential Equations.- First-Order Partial Differential Equations.- Solvable Partial Differential Equations.- The Canonical Forms.- The Method of Separation of Variables.- The One-Dimensional Heat Equation.- The One-Dimensional Heat Equation (Cont’d.).- The One-Dimensional Wave Equation.- The One-Dimensional Wave Equation (Cont’d.).- Laplace Equation in Two Dimensions.- Laplace Equation in Polar Coordinates.- Two-Dimensional Heat Equation.- Two-Dimensional Wave Equation.- Laplace Equation in Three Dimensions.- Laplace Equation in Three Dimensions (Cont’d.).- Nonhomogeneous Equations.- Fourier Integral and Transforms.- Fourier Integral and Transforms (Cont’d.).- Fourier Transform Method for Partial DEs.- Fourier Transform Method for Partial DEs (Cont’d.).- Laplace Transforms.- Laplace Transforms (Cont’d.).- Laplace Transform Method for Ordinary DEs.- Laplace Transform Method for Partial DEs.- Well-PosedProblems.- Verification of Solutions.

From the reviews: "This work by Agarwal (Florida Institute of Technology) and O'Regan ... gives a clear introduction to the fields of study identified in its title. ... The authors provide 50 short lectures on various topics in the theory of ordinary and partial differential equations. This format makes independent reading of the book easier since it condenses the material into sections of manageable length. ... Beginning graduate students would be the ideal audience for such self-study. Summing Up: Recommended. Academic audiences, upper-division undergraduates and above." (S. L. Sullivan, Choice, Vol. 47 (1), September, 2009) "The book comprises 50 class-tested lectures which both the authors have given to engineering and mathematics major students under the titles Boundary Value Problems and Methods of Mathematical Physics at various institutions all over the globe ... . The prerequisite for this book is calculus, so it can be used for a senior undergraduate course. It should also be suitable for a beginning graduate course ... . The answers and hints to almost all the exercises are provided for the convenience of the reader." (Juri M. Rappoport, Zentralblatt MATH, Vol. 1172, 2009)