7 edition of Complex Analysis with MATHEMATICA® found in the catalog.
June 12, 2006 by Cambridge University Press .
Written in English
|The Physical Object|
|Number of Pages||571|
If your aim is to use complex variables for example in engineering and physics problems Whittaker and Watson is an excellent choice. Complex algebra and geometry; 3. The values of such a holomorphic function inside a disk can be computed by a path integral on the disk's boundary as shown in Cauchy's integral formula. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of many intriguing topics that are uncommon in a book at this level. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity.
Written in an informal style by a master expositor, the book distills more than half a century of experience with the subject into a lucid, engaging, yet rigorous account. Numerical transform techniques; As a result, the value of a holomorphic function over an arbitrarily small region in fact determines the value of the function everywhere to which it can be extended as a holomorphic function. There are no numbered equations. Elementary applications to two-dimensional physics;
It is of the same epoch as WW but written from a completely different point of view. The function on the larger domain is said to be analytically continued from its values on the smaller domain. It should appeal to anyone with an interest in the geometric side of complex analysis. Table of Contents Preface; 1. A complex view of the real logistic map; 6. D'Angelo was the winner of the Bergman Prize; he was cited for several important contributions to complex analysis, including his work on degenerate Levi forms and points of finite type, as well as work, some joint with David Catlin, on positivity conditions in complex analysis.
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Cubics, quartics and visualization of complex roots; 4. The function on the larger domain is said to be analytically continued from its values on the smaller domain.
Symmetric chaos in the complex plane; 8. Elementary applications to two-dimensional physics; His mathematical interests are number theory and classical analysis. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems.
Numerous examples, exercises, and discussions of geometric reasoning appear along the way. Detailed solutions of the exercises, included at the back of the book, both serve as models for students and facilitate independent study. You cannot claim that you understood something, until you solve a couple of problems.
It masterfully combines excellent expositions of the beauties and subtlety of complex analysis, and several of its applications to physical theory, with clear explanations of the flexibility and the power of Mathematica for computing and for generating marvellous graphical displays.
Sometimes, as in the case of the natural logarithmit is impossible to analytically continue a holomorphic function to a non-simply connected domain in the complex plane but it is possible to extend it to a holomorphic function on a closely related surface known as a Riemann surface.
If a function has such a pole, then one can compute the function's residue there, which can be used to compute path integrals involving the function; this is the content of the powerful residue theorem.
He has 2 separate small books of exercises. Newton-Raphson iteration and complex fractals; 5. These requirements correspond to requiring that we consider only curves that can be traced, such as by a pen, in a sequence of even, steady strokes, which only stop to start a new piece of the curve, all without picking up the pen.
It begins on a very basic level, but ends with more advanced material then all other texts that I mention the things which are covered nowadays under the title Riemann surfaces, and not included in CV textbooks anymore. Laplace transforms; This allows the extension of the definition of functions, such as the Riemann zeta functionwhich are initially defined in terms of infinite sums that converge only on limited domains to almost the entire complex plane.
A contour is a directed curve which is made up of a finite sequence of directed smooth curves whose endpoints are matched to give a single direction. Laurent series, zeroes, singularities and residues; The values of such a holomorphic function inside a disk can be computed by a path integral on the disk's boundary as shown in Cauchy's integral formula.
Language: English. In fact, a given smooth curve has only two such orderings.In complex analysis a contour is a type of curve in the complex plane. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined.
A curve in the complex plane is defined as a continuous function from a closed interval of the real line to the complex plane: z: [a, b] → C. COMPLEX ANALYSIS: for Mathematics & Engineering 3rd Ed,ISBN: Jones and Bartlett Publishers, Inc.
You need to use F(Z) - The Complex Variables Program, Maple or Mathematica to run these files. Chapter Headings. sylvaindez.comx analysis is in my opinion one of the most beautiful areas of mathemat-ics. It has one of the highest ratios of theorems to de nitions (i.e., a very low \entropy"), and lots of applications to things that seem unrelated to complex numbers, for example: Solving cubic equations that have only real roots (historically, this was the.
Complex Analysis with Mathematica by William T. Shaw. Publisher: Cambridge University Press Year: The included CD contains a live version of the book with all of the Mathematica code, allowing users to run computer experiments.
Teachers can utilize the book for a traditional course, with Mathematica as a tool for illustration or for. ComplexPlot uses a cyclic color function over Arg [f] to identify features such as zeros, poles and essential singularities.
The color function goes from to counterclockwise around zeros, clockwise around poles and infinite cycles near essential singularities.; ComplexPlot treats the variable z as local, effectively using Block.; ComplexPlot has attribute HoldAll, and evaluates f only after.
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