[...]... by most engineering departments Considering that the audience in these coumes comes from all subdisciplines of physics and engineering, the content and the level of mathematical formalism has t o be chosen very carefully Recently the growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance and has increased the demand for these... cc However, brain size and intelligence are only correlated loosely A much more stringent limit to our mental capacity naturally comes from the inner efficiency of our brain Research on subjects like brain stimulators, hard wiring of our brain, and mind reading machines are all aiming a t a faster and much more efficient use of our brain A better understanding of our brain may also bring a more efficient... selected and should be considered an integral part of the learning process In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics In fact, the number of books, old and new, written on this subject shows how dynamic this field is Naturally this book carries an imprint of my style and lectures Because the main aim of... researchers and instructors who want to add something new and interesting t o their course, this self-contained chapter is an excellent place to start Chapter 15 contains a comprehensive discussion of infinite series: tests of convergence, properties, power series, and uniform convergence along with the methods of evaluating sums of infinite series An interesting section on divergent series in physics... problems, and the Rayleigh-Ritz method are among other interesting topics covered In Chapter 18 we introduce integral equations We start with their classification and their relation to differential equations and vice versa We continue with the methods of solving integral equations and conclude with the eigenvalue problem for integral operators, that is, the Hilbert-Schmidt theory In Chapter 19 (and 20)... with interesting examples like the fringe effects of a parallel plate capacitor and fluid flow around an obstacle We also discuss complex integrals, series, and analytic continuation along with the methods of evaluating some definite integrals Chapter 14 introduces the basics of fractional calculus After introducing xxiv PREFACE the experimental motivation for why we need fractional derivatives and integrals,... many interesting and stimulating discussions, encouragement, and critical reading of the chapter on path integrals I thank Wiley for the support by a grant during the preparation of the camera ready copy My special thanks go t o my editors a t Wiley, Steve Quigley, Susanne Steitz, and Danielle Lacourciere for sharing my excitement and their utmost care in bringing this book into existence I finally... have covered important distance in understanding and controlling our genetic code To understand and codify ideas in terms of some basic physical processes naturally requires a significantly deeper level of understanding of our brain and its processes If ideas could be linked to certain physical processes at the molecular and cellular level, then there could also exist a finite upper limit to the number... the science and engineering undergraduate curriculum These basically comprise the contents of the books Advanced Calculus by Kaplan, Introductory Complex Analysis by Brown and Churchill, and Diflerential Equations by Ross, or the contents of books like Mathematicab Methods in Physical Sciences by Boas, Mathematical Methods: f o r Students of Physics and Related Fields by Hassani, and Essential Mathematical. .. expressed as inequalities like the uncertainty principle: AxAp 2 h and the second law of entropy: SS( total entropy of the universe) 2 0 (1.4) Others, which are expressed in terms of equalities, are theories or models based on certain assumptions and subject to change in time MATHEMATICS AND MIND 1.3 5 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing . h0" alt="" MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING This Page Intentionally Left Blank MATHEMATICAL METHODS IN SCIENCE AND ENGINEERG S Expressed as Diflerintegrals 421 Differint egrals 423 424 xiv CONTENTS 14.7 Applications of Diflerintegrals in Science and Engineering 424 14.7.2