||boek: Theory and Problems of Complex Variables|with an introduction to Conformal Mapping and its applications|Schaum's Outline Series

||door: Murray R. Spiegel

||taal: en
||jaar: 1964
||druk: ?
||pag.: 313p
||opm.: paperback|used|format A4

||isbn: N/A
||code: 1:002527

--- Over het boek (foto 1): Theory and Problems of Complex Variables ---

!description may be of another edition!

Master complex variables with "Schaum's" - the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love "Schaum's Outlines" because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use "Schaum's!" If you don't have a lot of time but want to excel in class, this book helps you: brush up before tests; find answers fast; study quickly and more effectively; and get the big picture without spending hours poring over lengthy textbooks. "Schaum's Outlines" give you the information your teachers expect you to know in a handy and succinct format - without overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, "Schaum's" let you study at your own pace and remind you of all the important facts you need to remember - fast! And "Schaum's" are so complete, they're perfect for preparing for graduate or professional exams. Inside, you will find: 640 problems, including step-by-step solutions; hundreds of additional practice problems, with answers supplied; clear explanations of complex variable theory; and understandable coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions. If you want top grades and thorough understanding of complex variables, this powerful study tool is the best tutor you can have! Chapters include: Complex Numbers; Functions, Limits, and Continuity; Limits and Continuity; Complex Differentiation and the Cauchy-Riemann Equations; Complex Integration and Cauchy's Theorem; Cauchy's Integral Formulas and Related Theorems; Infinite Series; Taylor's and Laurent's Series; The Residue Theorem; Evaluation of Integrals and Series; Conformal Mapping; Physical Applications of Conformal Mapping; Special Topics; and Index.

[source: https--www.amazon.com.be]

It's a good start, but beware the mistakes [2014-03-23]

This contains lots of examples of physical applications using conformal mappings, which ultimately is what any engineer would need. It also touches on (in some cases lightly) most (if not all) approaches to the definition and analysis of the complex plane, but in some cases rather too lightly to be used as a sole text for self-education.

There are also some mistakes which could cause considerable confusion:
"Show that Re(sin^-1 z) = 1/2 (sqrt(x^2 + y^2 + 2 x + 1) - sqrt(x^2 + y^2 - 2 x + 1) )
which is egregious -- I spent the thick end of a week chasing down some violently sticky algebra before finally giving up and looking at it backward and suddenly realising that what it should have been was Re(tanh^-1 z) or something, and even then it looks wrong.

As a supplement to an existing set of texts within the context of a tutored class, then it's a worthwhile purchase.

Matt Westwood [source: https--www.amazon.com]

An excellent book for learning how to use complex analysis to solve problems [2023-12-04]

This was the book that I used for my first complex variables course as an undergraduate, and I still turn back to it for practice.

Unlike a complex analysis book, or even more typical complex variables book, the focus is really not on the theory. Learning how to prove theorems is not the point of the book, so each section does give a rundown of what the relevant theorems, state and examples of how to use them before giving a whole bunch of problems to practice on.

The professor of that class was extremely focused on problem solving techniques over understanding much beyond how to extend things like line integrals and geometric series to solving problems. When I retook the course for a refresher before beginning my analysis sequencing graduate school, I didn't find myself at much of a loss at all when it came to the theory. Part of the reason is that I had another terrific for professor, but part of the reason is also that I had already learned how to do the problems. It's a good approach, along the same vein as how we teach students calculus before we teach them analysis: having a basic familiarity with how the problems works helps to understand what the theorems actually do, which it easier for me to understand what was going on in the proofs.

I would not recommend this book to learn the subject for the first time, necessarily, at least not without lecture notes to assist. However, it's excellent as a refresher and as a tool for studying, not only because it gives you a localized list of important theorems and examples of how they are applied, but because there are just so many problems to do.

Laurel Beth [source: https--www.amazon.com]

Contents

Preface

Chapter 1 COMPLEX NUMBERS

The real number system. Graphical representation of real numbers. The complex number system. Fundamental operations with complex numbers. Absolute value. Axiomatic foundations of the complex number system. Graphical representation of complex numbers. Polar form of complex numbers. De Moivre's theorem. Roots of complex numbers. Euler's formula. Polynomial equations. The nth roots of unity. Vector interpretation of complex numbers. Spherical representation of complex numbers. Stereographic projection. Dot and cross product. Complex conjugate coordinates. Point sets.

Chapter 2 FUNCTIONS, LIMITS AND CONTINUITY

Variables and functions. Single-and multiple-valued functions. Inverse functions. Transformations. Curvilinear coordinates. The elementary functions. Branch points and branch lines. Riemann surfaces. Limits. Theorems on limits. Infinity. Continuity. Continuity in a region. Theorems on continuity. Uniform continuity. Sequences. Limit of a sequence. Theorems on limits of sequences. Infinite series.

Chapter 3 COMPLEX DIFFERENTIATION AND THE CAUCHY-RIEMANN EQUATIONS

Derivatives. Analytic functions. Cauchy-Riemann equations. Harmonic functions. Geometric interpretation of the derivative. Differentials. Rules for differentiation. Derivatives of elementary functions. Higher order derivatives. L'Hospital's rule. Singular points. Orthogonal families. Curves. Applications to geometry and mechanics. Complex differential operators. Gradient, divergence, curl and Laplacian. Some identities involving gradient, divergence and curl.

Chapter 4 COMPLEX INTEGRATION AND CAUCHY'S THEOREM

Complex line integrals. Real line integrals. Connection between real and complex line integrals. Properties of integrals. Change of variables. Simply-and multiply-connected regions. Jordan curve theorem. Convention regarding traversal of a closed path. Green's theorem in the plane. Complex form of Green's theorem. Cauchy's theorem. The Cauchy-Goursat theorem. Morera's theorem. Indefinite integrals. Integrals of special functions. Some consequences of Cauchy's theorem.

Chapter 5 CAUCHY'S INTEGRAL FORMULAE AND RELATED THEOREMS

Cauchy integral formulae. Some important theorems. Morera's theorem. Cauchy's inequality. Liouville's theorem. Fundamental theorem of algebra. Gauss' mean value theorem. Maximum modulus theorem. Minimum modulus theorem. The argument theorem. Rouché's theorem. Poisson's integral formulae for a circle. Poisson's integral formulae for a half plane.

Chapter 6 INFINITE SERIES. TAYLOR'S AND LAURENT SERIES

Sequences of functions. Series of functions. Absolute convergence. Uniform convergence of sequences and series. Power series. Some important theorems. General theorems. Theorems on absolute convergence. Special tests for convergence. Theorems on uniform convergence. Theorems on power series. Taylor's theorem. Some serial series. Laurent's theorem. Classification of singularities. Entire functions. Mesomorphic functions. Lagrange's expansion. Analytic continuation.

Chapter 7 THE RESIDUE THEOREM. EVALUATION OF INTEGRALS AND SERIES

Residues. Calculation of residues. The residue theorem. Evaluation of definite integrals. Serial theorems used in evaluating integrals. The Cauchy principal value of integrals. Differentiation under the integral sign. Leibnitz's rule. Summation of series. Mittag-Leffler's expansion theorem. Some special expansions.

Chapter 8 CONFORMAL MAPPING

Transformations or mappings. Jacobian of a transformation. Complex mapping functions. Conformal mapping. Riemann's mapping theorem. Fixed or invariant points of a transformation. Some general transformations. Translation. Rotation. Stretching. Inversion. Successive transformations. The linear transformation. The bilinear or fractional transformation. Mapping of a half plane on to a circle. The Schwarz-Christoffel transformation. Transformations of boundaries in parametric form. Some special mappings.

Chapter 9 PHYSICAL APPLICATIONS OF CONFORMAL MAPPING

Boundary-value problems. Harmonic and conjugate functions. Dirichlet and Neumann problems. The Dirichlet problem for the unit circle. Poisson's formula. The Dirichlet problem for the half plane. Solutions to Dirichlet and Neumann problems by conformal mapping. Applications to fluid flow. Basic assumptions. The complex potential. Equipotential lines and streamlines. Sources and sinks. Some special flows. Flow around obstacles. Bernoulli's theorem. Theorems of Blasius. Applications to electrostatics. Coulomb's law. Electric field intensity. Electrostatic potential. Gauss' theorem. The complex electrostatic potential. Line charges. Conductors. Capacitance. Applications to heat flow. Heat flux. The complex temperature.

Chapter 10 SPECIAL TOPICS

Analytic continuation. Schwarz's reflection principle. Infinite products. Absolute, conditional and uniform convergence of infinite products. Some important theorems on infinite products. Weierstrass' theorem for infinite products. Some special infinite products. The gamma function. Properties of the gamma function. The beta function. Differential equations. Solution of differential equations by contour integrals. Bessel functions. Legendre functions. The hypergeometric function. The zeta function. Asymptotic series. The method of steepest descents. Special asymptotic expansions. Elliptic functions.

INDEX

[source: https--proofwiki.org/wiki/Book:Murray_R._Spiegel/Theory_and_Problems_of_Complex_Variables/SI_(Metric)_Edition]

--- Over (foto 2): Murray R. Spiegel ---

Murray Ralph Spiegel (1923-1991) was an author of textbooks on mathematics, including titles in a collection of Schaum's Outlines.

Spiegel was a native of Brooklyn and a graduate of New Utrecht High School. He received his bachelor's degree in mathematics and physics from Brooklyn College in 1943. He earned a master's degree in 1947 and doctorate in 1949, both in mathematics and both at Cornell University. He was a teaching fellow at Harvard University in 1943[-]1945, a consultant with Monsanto Chemical Company in the summer of 1946, and a teaching fellow at Cornell University from 1946 to 1949. He was a consultant in geophysics for Beers & Heroy in 1950, and a consultant in aerodynamics for Wright Air Development Center from 1950 to 1954. Spiegel joined the faculty of Rensselaer Polytechnic Institute in 1949 as an assistant professor. He became an associate professor in 1954 and a full professor in 1957. He was assigned to the faculty Rensselaer Polytechnic Institute of Hartford, CT, when that branch was organized in 1955, where he served as chair of the mathematics department. His PhD dissertation, supervised by Marc Kac, was titled On the Random Vibrations of Harmonically Bound Particles in a Viscous Medium.

Works [Most Recent Edition: ####]

1956 Schaum's Outline of College Algebra [2018]
???? Schaum's Outline of College Physics
1961 Schaum's Outline of Statistics [2018]
1963 Schaum's Outline of Advanced Calculus [2010]
1964 Schaum's Outline of Complex Variables [2009]
1965 Schaum's Outline of Laplace Transforms
1968 Schaum's Mathematical Handbook of Formulas and Tables [2008]
1968 Schaum's Outline of Vector Analysis [And An Introduction to Tensor Analysis] [2009]
1969 Schaum's Outline of Real Variables
1971 Schaum's Outline of Advanced Mathematics for Engineers and Scientists [2009]
1971 Schaum's Outline of Finite Differences and Difference Equations
1974 Schaum's Outline of Fourier Analysis with Applications to Boundary-Value Problems
1975 Schaum's Outline of Probability and Statistics [2013]
1967 Schaum's Outline of Theoretical Mechanics
1963 Applied Differential Equations [1980]

[source: wikipedia]

Murray Ralph Spiegel était un auteur de manuels sur les mathématiques, y compris des titres dans une collection de Schaum's Outlines. Spiegel était originaire de Brooklyn et diplômé du New Utrecht High School. Il a obtenu son baccalauréat en mathématiques et physique du Brooklyn College en 1943.

[source: https--www.babelio.com/auteur/Murray-R-Spiegel/487247]

The Late MURRAY R. SPIEGEL received the M.S degree in Physics and the Ph.D. in Mathematics from Cornell University. He had positions at Harvard University, Columbia University, Oak Ridge and Rensselaer Polytechnic Insitute, and served as a mathematical consultant at several large Companies. His last Position was professor and Chairman of mathematics at the Rensselaer Polytechnic Institute Hartford Graduate Center. He was interested in most branches of mathematics at the Rensselaer polytechnic Institute, Hartford Graduate Center. He was interested in most branches of mathematics, especially those which involve applications to physics and engineering problems. He was the author of numerous journal articles and 14 books on various topics in mathematics.

[source: https--www.amazon.com]