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Mathematics - Dynamical Systems & Differential Equations | Ordinary and Partial Differential Equations - With Special Functions, Fourier Series, and Boundary

Ordinary and Partial Differential Equations

With Special Functions, Fourier Series, and Boundary Value Problems

Series: Universitext

Agarwal, Ravi P., O'Regan, Donal

2009

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  • Provides a genuine treatment of ODEs and PDEs aimed mainly towards applications
  • Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illustrations
  • Provides exercises at the end of each chapter for practice
  • Uses detailed examples to drive the presentation
  • Provides a theoretical treatment by organizing the material around theorems and proofs

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 80th 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.

Content Level » Graduate

Keywords » Boundary value problem - PDE - calculus - differential equation - linear optimization - ordinary differential equation - partial differential equation - verification - wave equation

Related subjects » Computational Intelligence and Complexity - Computational Science & Engineering - Dynamical Systems & Differential Equations - Theoretical, Mathematical & Computational Physics

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