Ebook: Ordinary and Partial Differential Equations: With Special Functions, Fourier Series, and Boundary Value Problems

This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures.

Key Features:

• Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illustrations.
• Develops ODEs in conjuction with PDEs and is aimed mainly toward applications.
• Covers importat applications-oriented topics such as solutions of ODEs in the form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomicals, Legendre, Chebyshev, Hermite, and Laguerre polynomials, and the theory of Fourier series.
• Provides exercises at the end of each chapter for practice.

This book is ideal for an undergratuate or first year graduate-level course, depending on the university. Prerequisites include a course in calculus.

About the Authors:

Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 800 journal articles and more than 20 books, and actively contributes to over 40 journals and book series in various capacities.

Donal O’Regan received his Ph.D. in mathematics from Oregon State University, Oregon, U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is the author/co-author of 15 books and has published over 650 papers on fixed point theory, operator, integral, differential and difference equations. He serves on the editorial board of many mathematical journals.

Previously, the authors have co-authored/co-edited the following books with Springer: Infinite Interval Problems for Differential, Difference and Integral Equations; Singular Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To V. Lakshmikanthan on his 80^th Birthday; An Introduction to Ordinary Differential Equations.

In addition, they have collaborated with others on the following titles: Positive Solutions of Differential, Difference and Integral Equations; Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations.

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Covers analytical techniques for solving single equation ODEs and some PDEs and is organized as 50 lectures. This is a good book for anyone who has already taken a one semester undergrad course on differential equations. The book claims all you need is calculus, but this claim is completely unrealistic as the authors skim through the contents of a differential equations course all in the first 46 pages! This sentence in the preface pretty much indicates who the intended audience is: "Like any other mathematical book, it does contain some theorems and their proofs". LOL. And true there aren't many theorems and of those theorems that are stated a good portion lack a proof. This book doesn't cover numerical methods nor uses anything requiring knowledge of linear algebra (eg, inner products and norms are used but you don't need to know what a vector space is). What is covered include series solutions, various special functions, Green's function, perturbation techniques, boundary value/Sturm Liouville, and solving PDEs centered around seperation of variables technique. Many exercises and hints/answers at the end of each chapter. There is one thing I really don't like about this book: If you aren't going to prove a major theorem, at least give a reference or have a section in the chapter for "further reading". All we get are statements along the lines of "the reason is beyond the scope of this book" or "this is too difficult to cover here" or "this requires advanced concepts"; no elaboration, no reference.