Civil Engineering Association

Advanced Engineering Mathematics with MATLAB, Second Edition
Dean G. Duffy
Chapman & Hall/CRC | English | 2003-03-28 | ISBN: 1584883499 | 840 pages | PDF | 18 MB


Resoundingly popular in its first edition, Dean Duffy's Advanced Engineering Mathematics has been updated, expanded, and now more than ever provides the solid mathematics background required throughout the engineering disciplines. Melding the author's expertise as a practitioner and his years of teaching engineering mathematics, this text stands clearly apart from the many others available. Relevant, insightful examples follow nearly every concept introduced and demonstrate its practical application. This edition includes two new chapters on differential equations, another on Hilbert transforms, and many new examples, problems, and projects that help build problem-solving skills. Most importantly, the book now incorporates the use of MATLAB throughout the presentation to reinforce the concepts presented. MATLAB code is included so readers can take an analytic result, fully explore it graphically, and gain valuable experience with this industry-standard software

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ADVANCED ENGINEERING MATHEMATICS with MATLAB

This book is an updated and expanded version of my Advanced Engineering Mathematics. I have taken this opportunity to correct misprints, rewrite some of the text,
and include new examples, problems, and projects. Of equal importance, however, is the addition of three new chapters so that the book can now be used in a wide variety of
differential equations and engineering mathematics courses. These courses normally occur after classes on the calculus of single, multivariable, and vector-valued functions.
The book begins with complex variables. All students need to know how to do simple arithmetic operations involving complex numbers; this is presented in the first two
sections of
Chapter 1. The remaining portions of this chapter focus on contour
integration. This material should be taught if the course is devoted to transform methods.After this introduction, subsequent chapters or sections follow from the goals of the
course. In its broadest form, there are two general tracks:
Differential Equations Course: Most courses on differential equations cover threegeneral topics: fundamental techniques and concepts, Laplace transforms, and separation
of variable solutions to partial differential equations. The course begins with first- and higher-order ordinary differential equations, Chapters 2 and 3, respectively. After some introductory remarks, Chapter 2 devotes itself to presenting general methods for solving first-order ordinary differential equations. These methods include separation of variables, employing the properties of homogeneous,
linear, and exact differential equations, and finding and using integrating factors. The reason most students study ordinary differential equations is for their use in elementary
physics, chemistry, and engineering courses. Because these differential equations contain constant coefficients, we focus on how to solve them in Chapter 3, along with a detailed
analysis of the simple, damped, and forced harmonic oscillator. Furthermore, we include the commonly employed techniques of undetermined coefficients and variation of parameters for finding particular solutions. Finally, the special equation of Euler and Cauchy is included because of its use in solving partial differential equations in spherical coordinates. After these introductory chapters, the course would next turn to Laplace transforms. Laplace
transforms are useful in solving nonhomogeneous differential equations where the initial conditions have been specified and the forcing function “turns on and off.” The general properties are explored in §§6.1 to 6.7; the actual solution technique is presented in §§6.8 and 6.9.
Most differential equations courses conclude with a taste of partial differential equations via the method of separation of variables. This topic usually begins with a quick
introduction to Fourier series, §§4.1 to 4.4, followed by separation of variables as it appliesto the heat (§§11.1–11.3), wave (§§10.1– 10.3), or Laplace’s equation (§§12.1–
12.3). The exact equation that is studied depends upon the future needs of the students.
Engineering Mathematics Course: This book can be used in a wide variety ofengineering mathematics classes. In all cases the student should have seen most of the material in Chapters 2 and 3. There are at least three possible combinations:
● Option A: The course is a continuation of a calculus reform sequence where elementary differential equations have been taught. This course begins with Laplace
transforms and separation of variables techniques for the heat, wave, and/or Laplace equations, as outlined above. The course then concludes with either vector calculus or
linear algebra. Vector calculus is presented in Chapter 13 and focuses on the gradient operator as it applies to line integrals, surface integrals, the divergence theorem, and Stokes’ theorem. Chapter 14 presents linear algebra as a method for solving systems of linear
equations and includes such topics as matrices, determinants, Cramer’s rule, and the
solution of systems of ordinary differential equations via the classic eigenvalue problem.
● Option B: This is the traditional situation where the student has already studied differential equations in another course before he takes engineering mathematics. Here
separation of variables is retaught from the general viewpoint of eigenfunction expansions. Sections 9.1–9.3 explain how any piecewise continuous function can be reexpressed in an eigenfunction expansion using eigenfunctions from the classic Sturm-Liouville
problem. Furthermore, we include two sections which focus on Bessel functions (§9.4) and Legendre polynomials (§9.5). These eigenfunctions appear in the solution
of partial differential equations in cylindrical and spherical coordinates, respectively. The course then covers linear algebra and vector calculus as given in Option A.
● Option C: I originally wrote this book for an engineering mathematics course given
to sophomore and junior communication, systems, and electrical engineering majors at
the U.S. Naval Academy. In this case, you would teach all of Chapter 1 with the possible exception of §1.10 on Cauchy principalvalue integrals. This material was added to
prepare the student for Hilbert transforms.
Because most students come to this course with a good knowledge of differential equations, we begin with Fourier series, Chapter 4, and proceed through Chapter 8. Chapter 5 generalizes the Fourier series to aperiodic functions and introduces the Fourier transform in
Chapter 5. This leads naturally to Laplace transforms, Chapter 6. Throughout these
chapters, I make use of complex variables in the treatment and inversion of the transforms. With the rise of digital technology and its associated difference equations, a version of the Laplace transform, the z-transform, was developed. Chapter 7 introduces the ztransform
by first giving its definition and then developing some of its general properties. We also illustrate how to compute the inverse by long division, partial
equations, especially with respect to the stability of the system. in communications, today’s engineer must have a command of this transform. The
Hilbert transform is introduced in §8.1 and its properties are explored in §8.2. Two
mportant applications of Hilbert transforms are introduced in §§8.3 and 8.4, namely theconcept of analytic signals and the Kramer-Kronig relationship. In addition to the revisions of the text and topics covered in this new addition, I now
incorporate the mathematical software package MATLAB to reinforce the concepts thatare taught. The power of MATLAB is its ability to quickly and easily present results in a
graphical format. I have exploited this aspect and now included code (scripts) so that the student fractions, and contour integration. Finally, we use z-transforms to solve difference Finally, I added a new chapter on the Hilbert transform. With the explosion of interest can explore the solution for a wide variety of parameters and different prospectives. Of course this book still continues my principle of including a wealth of examples from the scientific and engineering literature. The answers to the odd problems are given in the back of the book while worked solutions to all of the problems are available from the publisher. Most of the MATLAB scripts may be found at under
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Advanced Engineering Mathematics - 1st Edition