Universitext

Ordinary and Partial Differential Equations

With Special Functions, Fourier Series, and Boundary Value Problems

Authors: Agarwal, Ravi P., O'Regan, Donal

  • 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
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Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-79146-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-0-387-79145-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

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)


Table of contents (50 chapters)

  • Solvable Differential Equations

    Agarwal, Ravi P. (et al.)

    Pages 1-7

  • Second-Order Differential Equations

    Agarwal, Ravi P. (et al.)

    Pages 8-14

  • Preliminaries to Series Solutions

    Agarwal, Ravi P. (et al.)

    Pages 15-22

  • Solution at an Ordinary Point

    Agarwal, Ravi P. (et al.)

    Pages 23-30

  • Solution at a Singular Point

    Agarwal, Ravi P. (et al.)

    Pages 31-36

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-79146-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-0-387-79145-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ordinary and Partial Differential Equations
Book Subtitle
With Special Functions, Fourier Series, and Boundary Value Problems
Authors
Series Title
Universitext
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-79146-3
DOI
10.1007/978-0-387-79146-3
Softcover ISBN
978-0-387-79145-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 410
Number of Illustrations and Tables
35 b/w illustrations
Topics