Ordinary and Partial Differential Equations

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

ISBN 0387791450   Pages 428 ISBN13 9780387791456 (What's this?)   Volumes 1 Publisher Springer-Verlag New York Inc.   Weight (grammes) 597 Imprint Springer-Verlag New York Inc.   Published in New York, NY Format Paperback   Series title Universitext Publication date 01 Sep 2008   Height (mm) 234 Library of Congress 2008938952   Width (mm) 156 DEWEY 515.35   Spine width (mm) 22 DEWEY edition DC22   Academic level Undergraduate

1		Solvable Differential Equations		1
2		Second-Order Differential Equations		8
3		Preliminaries to Series Solutions		15
4		Solution at an Ordinary Point		23
5		Solution at a Singular Point		31
6		Solution at a Singular Point (Cont'd.)		37
7		Legendre Polynomials and Functions		47
8		Chebyshev, Hermite and Laguerre Polynomials		57
9		Bessel Functions		64
10		Hypergeometric Functions		75
11		Piecewise Continuous and Periodic Functions		83
12		Orthogonal Functions and Polynomials		90
13		Orthogonal Functions and Polynomials (Cont'd.)		95
14		Boundary Value Problems		104
15		Boundary Value Problems (Cont'd.)		109
16		Green's Functions		119
17		Regular Perturbations		129
18		Singular Perturbations		138
19		Sturm-Liouville Problems		145
20		Eigenfunction Expansions		157
21		Eigenfunction Expansions (Cont'd.)		163
22		Convergence of the Fourier Series		171
23		Convergence of the Fourier Series (Cont'd.)		176
24		Fourier Series Solutions of Ordinary Differential Equations		187
25		Partial Differential Equations		194
26		First-Order Partial Differential Equations		202
		More...

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)

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