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To Accompany Introduction to Integral Equations with Applications Second Edition Revised and Expanded Abdul J. Jerri Clarkson University Wiley Publishers San Diego New York Chicago 1999 |
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To Accompany Introduction to Integral Equations with Applications Second Edition Revised and Expanded Abdul J. Jerri Clarkson University Wiley Publishers San Diego New York Chicago 1999 |
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About the Author........
ABDUL J.JERRI is a Professor
of mathematics in the Department of Mathematics and Computer Science at
Clarkson University, Potsdam, New York. He is the author of three other
books besides the undergraduate textbook “Introduction to Integral Equations
with Applications - Second Edition, Wiley & Sons, Inc., 1999” for which
this Student’s Solutions Manual is prepared. For books of the author see
the last four pages of this book.
Dr. Jerri’s research interests
include the sampling expansion and its error analysis, integral and discrete
transforms, iterative methods for nonlinear problems and the Gibbs phenomenon.
He has authored more than forty research papers in these areas. Additionally,
he has lectured on these topics at many universities and at various national
conferences. He has also taught at three universities abroad.
Dr. Jerri is a member
of the American Mathematical Society and the Society of Industrial
and Applied Mathematics. He received the B.Sc. Degree in physics from the
University of Baghdad (1995), the M.Sc. Degree in physics form Illinois
Institute of Technology (1960), and the Ph.D. Degree in mathematics from
Oregon State University (1967).
Preface
This Student's Solution Manual is prepared to accompany and mainly supplement the second edition of the author's text "Introduction to Integral Equations with Applications - Revised and Expanded" by A.J. Jerri, Wiley & Sons, Inc. 1999". It contains detailed solutions to all the odd numbered problems in the text plus, occasionally, one even numbered problem in a section that may be of much importance to continuity of the subject discussed. These worked out problems are selected as representative of each section's exercise sets. Besides the exercises in the text we have also included solutions of other related problems in most of the sections under "Additional Solved Problems" with their statements and detailed solutions, and we placed them at the end of the exercises of their related section. These problems include some challenging or very detailed ones that may help widen the scope of the related subject in the text.
We may stress that this solutions manual is only to complement the essential step for solving the exercises, that is for the student to first attempt doing them before consulting this solutions manual. Of course, both of these steps should come after studying the notes of the instructor on the particular section followed by reading that subject in the text, and last but not least studying and understanding the detailed examples in the text. Many of the exercises can be approached with much ease after such understanding of the examples with the help of the (very often given) detailed hints at the end of each exercise.
The solutions here are by no means the shortest or the only way of solving, and the student is encouraged to find other possible methods for the solutions, where answers are provided at the end of the text for all the exercises.
For a fast convenient reference to the needed basic
trigonometric identities and integrals for the solutions in this manual,
we have listed most of them in the Appendix at the end of this Solutions
Manual.
(See Other books of the author following the Appendix.)
A.J. Jerri
Potsdam, New York, June , 1999
Table of Contents
| Preface |
| 1 Integral Equations, Origin and Basic Tools |
| Exercises 1.1, p. 3: Various Problems as Integral Equations |
| 1.1.A. Additional Solved Problems for Section 1.1: Various Problems as Integral Equations |
| Exercises 1.2: Classification of Integral Equations |
| 1.2.A. Additional Solved Problems for Section 1.2: Classification of Integral Equations |
| Exercises 1.3: some Important Identities and Definitions |
| 1.3.A. Additional Solved Problems for Section 1.3: Some Important Identities |
| Exercises 1.3: Laplace, Fourier, and Other Transforms |
| 1.4.A. Additional Solved Problems for Section 1.4: Laplace, Fourier, and Other Transforms |
| Exercises 1.5, p. 94 Basic Numerical Integration Formulas |
| 2 Modeling of Problems as Integral Equations |
| Exercises 2.1, p. 101: Population Dynamics |
| Exercises 2.2, p. 103: Control and Other Problems |
| Exercises 2.3, p. 112: Mechanics Problems |
| Exercises 2.4, p. 116: Initial Value Problems Reduced to Volterra Integral Equations |
| 2.4.A. Additional Solved Problems for Section 2.4: Initial Value Problems Reduced to Volterra Integral Equations |
| Exercises 2.5, p. 122: Boundary Value Problems Reduced to Fredholm Integral Equations |
| 2.5.A. Additional Solved Problems for Section 2.5: Boundary Value Problems Reduced to Fredholm Integral Equations |
| Exercises 2.6, p. 127: Mixed Boundary Conditions: Dual Integral Equations |
| 2.6.A. Additional Solved Problems for Section 2.6: Mixed Boundary Conditions - Dual Integral Equations |
| 3 Volterra Integral Equations |
| Exercises 3.1, p. 146: Volterra Integral Equations of the Second Kind |
| 3.1.A. Additional Solved Problems for Section 3.1: Volterra Integral Equations of the Second Kind |
| Exercises 3.2, p. 154: Volterra Integral Equations of the First Kind |
| 3.2.A. Additional Solved Problems for Section 3.2: Volterra Integral equation of the First Kind |
| Exercises 3.3, p. 156: Numerical Solutions of Volterra Integral Equations |
| 3.3.A. Additional Solved Problems for Section 3.3: Numerical Solutions of Volterra Integral Equations |
| 4 The Green's Function |
| Exercises 4.1, p. 193: Construction of the Green's Function |
| 4.1.A. Additional Solved Problems for Section 4.1: Construction of Green's Function |
| Exercises 4.2, p. 200: Fredholm Integral Equations and the Green's Function |
| 5 Fredholm Integral Equations |
| Exercises 5.1, p. 232: Fredholm Integral Equations with Degenerate Kernel |
| Exercises 5.2, p. 251: Fredholm Integral Equations with Symmetric Kernel |
| 5.2.A. Additional Solved Problems for Section 5.2: Fredholm Equations with Symmetric Kernel |
| Exercises 5.3, p. 268: Fredholm Integral Equations of the Second Kind |
| Exercises 5.4, p. 281: Fredholm Integral Equaitons of the First Kind |
| 5.4.A. Additional Solved Problems for Section 5.4: Fredholm Integral Equations of the First Kind |
| Exercises 5.5, p. 295: Numerical Solutions of Fredholm Integral Equations |
| 5.5.A. Additional Solved Problems for Chapter 5: Some Singular Fredholm Integral Equations |
| 7 Quadrature Rules for the Numerical Solutions |
| Exercises 7.1, p. 348: Higher Quadrature Rules of Integration with Tables |
| Exercises 7.2, p. 357: Higher Quadrature Rules for Volterra Integral Equations |
| 7.2.A. Additional Solved Problems for Section 7.2: Higher Quadrature Rules for Volterra Integral Equations |
| Exercises 7.3, p. 370: Higher Quadrature Rules for Fredholm Integral Equations |
| 7.3.A. Additional Solved Problems for Section 7.3: Higher Quadrature Rules for Fredholm Integral Equations |
| Appendix A: The Hankel Transforms |
| Exercises Appendix A, p. 376 |
| Appendix: Trigonometric Identities and Some Basic Integrals |
Other Books by the Author
The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approxiamations, Kluwer Academic Publishers, Boston, 320p.
Introduction to Integral Equations with Applications- Second Edition, Wily& Sons Inc., 1999, 450p.
Linear Difference Equations with Discrete Transform Methods, Kluwer Academic Publishers, Boston, 1996, 465p.
Integral and Discrete Transforms with Applications and Error Analysis, Marcel-Dekker Inc., New York, 1992, 885p.