Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Edition) 3rd Edition by Edward B. Saff (PDF)

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This is the best seller in this market. It provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books–both in level of exposition and layout–it incorporates physical applications throughout the presentation, so that the mathematical methodology appears less sterile to engineering students.

User’s Reviews

Editorial Reviews: From the Back Cover This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems and is designed to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books–both in level of exposition and layout–it incorporates physical applications throughout, so that the mathematical methodology appears less sterile to engineers. It makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic/analytic discussion of all topics. A downloadable MATLAB toolbox–a state-of-the-art computer aid–is available. Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations for Analytic Functions. Residue Theory. Conformal Mapping. The Transforms of Applied Mathematics. MATLAB ToolBox for Visualization of Conformal Maps. Numerical Construction of Conformal Maps. Table of Conformal Mappings. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (e.g., AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and the Sokhotskyi-Plemeij formulas. For mathematicians and engineers interested in Complex Analysis and Mathematical Physics. Excerpt. © Reprinted by permission. All rights reserved. The raison d’existence for Fundamentals of Complex Analysis with Applications to Engineering and Science, 3/e is our conviction that engineering, science, and mathematics undergraduates who have completed the calculus sequence are capable of understanding the basics of complex analysis and applying its methods to solve engineering problems. Accordingly, we address ourselves to this audience in our attempt to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. To accomplish this goal we have modeled the text after standard calculus books, both in level of exposition and layout, and have incorporated engineering applications throughout the text so that the mathematical methodology will appear less sterile to the reader. To be more specific about our mode of exposition, we begin by addressing the question most instructors ask first: To what extent is the book self contained, i.e., which results are proved and which are merely stated? Let us say that we have elected to include all the proofs that reflect the spirit of analytic function theory and to omit most of those that involve deeper results from real analysis (such as the convergence of Riemann sums for complex integrals, the Cauchy criterion for convergence, Goursat’s generalization of Cauchy’s theorem, or the Riemann mapping theorem). Moreover, in keeping with our philosophy of avoiding pedantics, we have shunned the ordered pairs interpretation of complex numbers and retained the more intuitive approach (grounded in algebraic field extensions). Cauchy’s theorem is given two alternative presentations in Chapter 4. The first is based on the deformation of contours, or what is known to topologists as homotopy. We have taken some pains to make this approach understandable and transparent to the novice because it is easy to visualize and to apply in specific situations. The second treatment interprets contour integrals in terms of line integrals and invokes Green’s theorem to complete the argument. These parallel developments constitute the two parts of Section 4 in Chapter 4; either one may be read, and the other omitted, without disrupting the exposition (although it should not be difficult to discern our preference, from this paragraph). Steady state temperature patterns in two dimensions are, in our opinion, the most familiar instances of harmonic functions, so we have principally chosen this interpretation for visualization of the theorems of analytic function theory. This application receives attention throughout the book, with special emphasis in Chapter 7 in the context of conformal mapping. There we draw the distinction between direct methods, wherein a mapping must be constructed to solve a specific problem, and indirect methods that postulate a mapping and then investigate which problems it solves. In doing so we hope to dispel the impression, given in many older books, that all applications of the technique fall in the latter category. In this third edition L. N. Trefethen and T. Driscoll have updated an appendix that reflects the progress made in recent years on the numerical construction of conformal mappings. A second appendix compiles a listing of some useful mappings having closed form expressions. Linear systems analysis is another application that recurs in the text. The basic ideas of frequency analysis are introduced in Chapter 3 following the study of the transcendental functions; Smith charts, circuit synthesis, and stability criteria are addressed at appropriate times; and the development culminates in Chapter 8 with the exposition of the analytic-function aspects of Fourier, Mellin, Laplace, Hilbert, and z transforms, including new applications in signal processing and communications. We hope thereby that our book will continue to serve the reader as a reference resource for subsequent coursework in these areas. Features of the Third Edition Novel features of the third edition are a discussion of the Riemann sphere, adding substance to the pragmatic concept of the “point at infinity” in complex analysis; an introduction to functional iteration and the picturesque Julia sets that thereby manifest themselves in the complex plane; an early exploration of the enrichment that the complex viewpoint provides in the analysis of polynomials and rational functions; and an introductory survey of harmonic function methods for calculating equilibrium temperatures for simple geometries. Optional sections are indicated with an asterisk so that readers can select topics of special interest. Summaries and suggested readings appear at the end of each chapter. As in previous editions, the text is distinguished by its wealth of worked-out examples that illustrate the theorems, techniques, and applications of complex analysis. Instructors (and curious students) may benefit from a MATLAB toolbox developed by Francisco Cameras, available by Internet download from the web site ee.eng.usf/people/snider2.html (click on complextools.zip). Instructions for its use are detailed in the file compman.doc. The toolbox provides graphic onscreen visualizations and animations of the algebraic manipulations of complex numbers and the common conformal maps, as well as a introductory guide for designing Joukowski airfoils. A downloadable .pdf file of the inevitable errata that our helpful readers report to us is also available at this site. The authors wish to acknowledge our mentors, Joseph L. Walsh and Paul Garabedian, who have inspired our careers, and to express their gratitude to Samuel Garrett, our longtime colleague at the University of South Florida; to acquisitions editor George Lobell for encouraging this project; to Adam Lewenberg for providing the art work and technical support; to our production editor Bob Waiters for his guidance in converting this work from manuscript to book; and to the following mathematicians, whose critical commentary contributed enormously to the development of the text: Carlos Berenstein, University of Maryland Keith Kearnes, University of Colorado Dmitry Khavinson, University of Arkansas Donald Marshall, University of Washington (Chapters 1-4, only) Mihai Putinar, University of California at Santa Barbara Sergei Suslov, Arizona State University Rebecca Wahl, Butler University G. Brock Williams, Texas Tech University Excerpt. © Reprinted by permission. All rights reserved. The raison d’existence for Fundamentals of Complex Analysis with Applications to Engineering and Science, 3/e is our conviction that engineering, science, and mathematics undergraduates who have completed the calculus sequence are capable of understanding the basics of complex analysis and applying its methods to solve engineering problems. Accordingly, we address ourselves to this audience in our attempt to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. To accomplish this goal we have modeled the text after standard calculus books, both in level of exposition and layout, and have incorporated engineering applications throughout the text so that the mathematical methodology will appear less sterile to the reader. To be more specific about our mode of exposition, we begin by addressing the question most instructors ask first: To what extent is the book self contained, i.e., which results are proved and which are merely stated? Let us say that we have elected to include all the proofs that reflect the spirit of analytic function theory and to omit most of those that involve deeper results from real analysis (such as the convergence of Riemann sums for complex integrals, the Cauchy criterion for convergence, Goursat’s generalization of Cauchy’s theorem, or the Riemann mapping theorem). Moreover, in keeping with our philosophy of avoiding pedantics, we have shunned the ordered pairs interpretation of complex numbers and retained the more intuitive approach (grounded in algebraic field extensions). Cauchy’s theorem is given two alternative presentations in Chapter 4. The first is based on the deformation of contours, or what is known to topologists as homotopy. We have taken some pains to make this approach understandable and transparent to the novice because it is easy to visualize and to apply in specific situations. The second treatment interprets contour integrals in terms of line integrals and invokes Green’s theorem to complete the argument. These parallel developments constitute the two parts of Section 4 in Chapter 4; either one may be read, and the other omitted, without disrupting the exposition (although it should not be difficult to discern our preference, from this paragraph). Steady state temperature patterns in two dimensions are, in our opinion, the most familiar instances of harmonic functions, so we have principally chosen this interpretation for visualization of the theorems of analytic function theory. This application receives attention throughout the book, with special emphasis in Chapter 7 in the context of conformal mapping. There we draw the distinction between direct methods, wherein a mapping must be constructed to solve a specific problem, and indirect methods that postulate a mapping and then investigate which problems it solves. In doing so we hope to dispel the impression, given in many older books, that all applications of the technique fall in the latter category. In this third edition L. N. Trefethen and T. Driscoll have updated an appendix that reflects the progress made in recent years on the numerical construction of conformal mappings. A second appendix compiles a listing of some useful mappings having closed form expressions. Linear systems analysis is another application that recurs in the text. The basic, ideas of frequency analysis are introduced in Chapter 3 following the study of the transcendental functions; Smith charts, circuit synthesis, and stability criteria are addressed at appropriate times; and the development culminates in Chapter 8 with the exposition of the analytic-function aspects of Fourier, Mellin, Laplace, Hilbert, and z transforms, including new applications in signal processing and communications. We hope thereby that our book will continue to serve the reader as a reference resource for subsequent coursework in these areas. Features of the Third Edition Novel features of the third edition are a discussion of the Riemann sphere, adding substance to the pragmatic concept of the “point at infinity” in complex analysis; an introduction to functional iteration and the picturesque Julia sets that thereby manifest themselves in the complex plane; an early exploration of the enrichment that the complex viewpoint provides in the analysis of polynomials and rational functions; and an introductory survey of harmonic function methods for calculating equilibrium temperatures for simple geometries. Optional sections are indicated with an asterisk so that readers can select topics of special interest. Summaries and suggested readings appear at the end of each chapter. As in previous editions, the text is distinguished by its wealth of worked-out examples that illustrate the theorems, techniques, and applications of complex analysis. Instructors (and curious students) may benefit from a MATLAB toolbox developed by Francisco Cameras, available by Internet download from the web site http://ee.eng.usf.edu/people/snider2.html (click on complextools.zip). Instructions for its use are detailed in the file compman.doc. The toolbox provides graphic onscreen visualizations and animations of the algebraic manipulations of complex numbers and the common conformal maps, as well as a introductory guide for designing Joukowski airfoils. A downloadable .pdf file of the inevitable errata that our helpful readers report to us is also available at this site. The authors wish to acknowledge our mentors, Joseph L. Walsh and Paul Garabedian, who have inspired our careers, and to express their gratitude to Samuel Garrett, our longtime colleague at the University of South Florida; to acquisitions editor George Lobell for encouraging this project; to Adam Lewenberg for providing the art work and technical support; to our production editor Bob Walters for his guidance in converting this work from manuscript to book; and to the following mathematicians, whose critical commentary contributed enormously to the development of the text: Carlos Berenstein, University of Maryland Keith Kearnes, University of Colorado Dmitry Khavinson, University of Arkansas Donald Marshall, University of Washington (Chapters 1-4, only) Mihai Putinar, University of California at Santa Barbara Sergei Suslov, Arizona State University Rebecca Wahl, Butler University G. Brock Williams, Texas Tech University E. B. Saff esaff@math.vanderbilt.edu A. D. Snider snider@eng.usf.edu Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I found out about this book from the OCW MIT course on complex analysis, and I must say it was a great find. The book I used to learn complex analysis is “Complex Variables with Applications” by Wunsch, which I also believe to be a good book, however this book by Edward Saff is much easier to understand. The writting style is very clear, and the material is carefully selected for engineering students.The book may fall a little short with the amount and depth of the topics, so math students who require lots of rigorous proofs may want to look somewhere else, however if you are an engineering or physics student the topics at hand will be perfectly covered at an introductory level.The only real complain about the book would be the physical book itself, as with most Pearson books, this book has one of the worst bindings I’ve ever seen, just like Griffith’s book “Introduction to Electrodynamics” (Also from Pearson editorial), the pages basically separate or unglue from the spine the second you open up the book, I had to use epoxy glue to keep the pages from falling off!!!! This seems to be a recurring problem with Pearson books, and somehow it seems Pearson doesnt care and year after year they continue to provide cheap binding on expensive hardcover books, thats really an unethical business scheme, one would only expect such low quality binding from cheap international edition books, yet it seems that in this case the international edition books have better manufacturing than the hardcover US editions for just a fraction of the price!My advice: Get the international edition of this book, if Pearson really wants us to pay the full price for their books, they should provide us with something worthy, not this, I wont be buying any hardcover Pearson textbook until they fix this issue.

⭐This book is very well written. It is one of the best textbooks for undergraduate complex analysis, appropriate for third year math majors, or mathematically experienced engineering or physics majors, who have some experience with proofs and epsilon-delta arguments prior to taking this course. It approaches the subject from a very traditional point of view. It is now several decades old and is beginning to feel a little bit dated. Most of the book is quite nice, but the graphics need to be updated, and the chapters on transformations of applied mathematics need to be rewritten. I like the book enough to use it again this year to teach the undergraduate complex analysis course at my university, although I am keeping my eye out for a more modern book that is as well written.

⭐This book is geared at an undergraduate audience and written at roughly the same level as a first course in real analysis, though with emphasis on computational problems and applications similar to a typical calculus class.That being said, this book is even quite useful at the graduate level. This book alone will get you at least halfway towards passing your qualifying exam in complex analysis. It has probably the best selection of problems out there for doing contour integrals via the residue theorem (it devotes a whole chapter to various integration strategies!). Ditto for conformal mappings–it devotes a whole appendix to a catolog of common conformal maps–and Laurent series. There is also solid though not deep treatment of the basics of the theory (Cauchy integral formula, Liouville theorem, Poisson integral formula, maximum modulus principle, etc.).Overall, this book is very well written and well organized. For the record, Saff is a very prolific and respected research mathematician.

⭐Saff and Snider really did an amazing job explaining complex analysis in good amount of depth for an undergraduate senior or junior.

⭐this book is a great supplement to any of the Complex analysis Books. It is written for the student to learn from and not for the author to impress his colleagues as most other books are. The language is clear and concise, and the multitude of problems help to reinforce the material

⭐good real world examples

⭐This textbook helps beginners immensely with learning Complex Analysis. I would recommend this book as it starts out slow and progresses over time.

⭐This textbook is full of everything from the proofs, to examples, to applications of Complex variables. Great supplement to electrical engineering curricula.

⭐There was an odd little thing on the top corner of the book, im not sure what it was but it was most likely glued on to it to make the book look good? Anyways, Saff wrote a brilliant book that shows the beauty of complex analysis. Would recommend!

⭐Edizione indiana che contiene tutto tranne le due appendici. La qualità della carta non è il massimo, come si può vedere dalle foto: il contenuto della pagina traspare a causa della grammatura forse non proprio ideale. A parte questo direi proprio che è un acquisto appropriato.Per quanto riguarda le SOLUZIONI degli esercizi, si trovano agevolmente e gratuitamente sul web (anche risolti per esteso).Nothing actuallyI used for myself in class

⭐A very concise book with interesting and challenging exercises. Used it in College and I had to buy a copy for my personal library.

⭐I purchased this book recently and it looked nice at first glance but once I began using it, the binding began to break and pages began to fall out. Secondly, the low quality pages are all really thin and are see through. So on certain pages I find it difficult to read.I won’t be ordering a book from amazon again.

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