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Partial Differential Equations for Scientists and Engineers



Partial Differential Equations for Scientists and Engineers PDF

Author: Stanley J. Farlow

Publisher: Dover Publications

Genres:

Publish Date: September 1, 1993

ISBN-10: 048667620X

Pages: 448

File Type: PDF

Language: English

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Book Preface

Over the last few years, there has been a significant increase in the number of students studying partial differential equations at the undergraduate level, and many of these students have come from areas other than mathematics, where intuition rather than mathematical rigor is emphasized. In writing Partial Dif­ferential Equations for Scientists and Engineers, l have tried to stimulate intuitive thinking, while, at the same time, not losing too much mathematical accuracy. At one extreme, it is possible to approach the subject on a high mathematical epsilon-delta level, which generally results in many undergraduate students not knowing what’s going on. At the other extreme, it is possible to wave away all the subtleties until neither the student nor the teacher knows what’s going on. I have tried to steer the mathematical thinking somewhere between these two extremes.
Partial Differential Equations for Scientists and Engineers evolved from a set of lecture notes I have been preparing for the last five years. It is an uncon­ventional text in one regard: It is organized in 47 semi-independent lessons in contrast to the more usual chapter-by-chapter approach.
Separation of variables and integral transforms are the two most important analytic tools discussed. Several nonstandard topics, such as Monte Carlo meth? ods, calculus of variations, control theory, potential theory, and integral equa­tions, are also discussed because most students will eventually come across these subjects at some time in their studies. Unless they study these topics here, they will probably never study them formally.
This book can be used for a one- or two-semester course at the junior or senior level. It assumes only a knowledge of differential and integral calculus and ordinary differential equations. Most lessons take either one or two days, so that a typical one-semester syllabus would be: Lessons 1-13, 15-17, 19-20, 22-23, 25-27, 30-32, 37-39. All 47 lessons can easily be covered in two semesters, with plenty of time to work problems.
The author wishes to thank the editors at Wiley for their invitation to write this book as well as the reviewers, Professor Chris Rorres and Professor M. Kursheed Ali, who helped me greatly with their suggestions. Any further sug­gestions for improvement of this book, either from students or teachers, would be greatly appreciated. Thanks also to Dorothy, Susan, Alexander, and Daisy Farlow.


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