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Ordinary and Partial Differential Equations

With Special Functions, Fourier Series, and Boundary Value Problems

  • Ravi P. Agarwal
  • Donal O’Regan

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Ravi P. Agarwal, Donal O’Regan
    Pages 1-7
  3. Ravi P. Agarwal, Donal O’Regan
    Pages 8-14
  4. Ravi P. Agarwal, Donal O’Regan
    Pages 15-22
  5. Ravi P. Agarwal, Donal O’Regan
    Pages 23-30
  6. Ravi P. Agarwal, Donal O’Regan
    Pages 31-36
  7. Ravi P. Agarwal, Donal O’Regan
    Pages 37-46
  8. Ravi P. Agarwal, Donal O’Regan
    Pages 47-56
  9. Ravi P. Agarwal, Donal O’Regan
    Pages 57-63
  10. Ravi P. Agarwal, Donal O’Regan
    Pages 64-74
  11. Ravi P. Agarwal, Donal O’Regan
    Pages 75-82
  12. Ravi P. Agarwal, Donal O’Regan
    Pages 83-89
  13. Ravi P. Agarwal, Donal O’Regan
    Pages 90-94
  14. Ravi P. Agarwal, Donal O’Regan
    Pages 95-103
  15. Ravi P. Agarwal, Donal O’Regan
    Pages 104-108
  16. Ravi P. Agarwal, Donal O’Regan
    Pages 109-118
  17. Ravi P. Agarwal, Donal O’Regan
    Pages 119-128
  18. Ravi P. Agarwal, Donal O’Regan
    Pages 129-137
  19. Ravi P. Agarwal, Donal O’Regan
    Pages 138-144
  20. Ravi P. Agarwal, Donal O’Regan
    Pages 145-156
  21. Ravi P. Agarwal, Donal O’Regan
    Pages 157-162
  22. Ravi P. Agarwal, Donal O’Regan
    Pages 163-170
  23. Ravi P. Agarwal, Donal O’Regan
    Pages 171-175
  24. Ravi P. Agarwal, Donal O’Regan
    Pages 176-186
  25. Ravi P. Agarwal, Donal O’Regan
    Pages 187-193
  26. Ravi P. Agarwal, Donal O’Regan
    Pages 194-201
  27. Ravi P. Agarwal, Donal O’Regan
    Pages 202-209
  28. Ravi P. Agarwal, Donal O’Regan
    Pages 210-218
  29. Ravi P. Agarwal, Donal O’Regan
    Pages 219-226
  30. Ravi P. Agarwal, Donal O’Regan
    Pages 227-233
  31. Ravi P. Agarwal, Donal O’Regan
    Pages 234-240
  32. Ravi P. Agarwal, Donal O’Regan
    Pages 241-248
  33. Ravi P. Agarwal, Donal O’Regan
    Pages 249-255
  34. Ravi P. Agarwal, Donal O’Regan
    Pages 256-265
  35. Ravi P. Agarwal, Donal O’Regan
    Pages 266-274
  36. Ravi P. Agarwal, Donal O’Regan
    Pages 275-283
  37. Ravi P. Agarwal, Donal O’Regan
    Pages 284-291
  38. Ravi P. Agarwal, Donal O’Regan
    Pages 292-299
  39. Ravi P. Agarwal, Donal O’Regan
    Pages 300-305
  40. Ravi P. Agarwal, Donal O’Regan
    Pages 306-315
  41. Ravi P. Agarwal, Donal O’Regan
    Pages 316-322
  42. Ravi P. Agarwal, Donal O’Regan
    Pages 323-329
  43. Ravi P. Agarwal, Donal O’Regan
    Pages 330-337
  44. Ravi P. Agarwal, Donal O’Regan
    Pages 338-343
  45. Ravi P. Agarwal, Donal O’Regan
    Pages 344-353
  46. Ravi P. Agarwal, Donal O’Regan
    Pages 354-360
  47. Ravi P. Agarwal, Donal O’Regan
    Pages 361-373
  48. Ravi P. Agarwal, Donal O’Regan
    Pages 374-383
  49. Ravi P. Agarwal, Donal O’Regan
    Pages 384-393
  50. Ravi P. Agarwal, Donal O’Regan
    Pages 394-398

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourne
  2. 2.GalwayMathematics DepartmentNational University of IrelandIreland

Bibliographic information