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  1. Home
  2. Books
  3. Complex Analysis with MATHEMATICA®
  • Cited by 14
Publisher:
Cambridge University Press
Online publication date:
August 2014
Print publication year:
2006
Online ISBN:
9781316036549
DOI:
https://doi.org/10.1017/CBO9781316036549
Subjects:
Mathematics, Real and Complex Analysis, Discrete Mathematics Information Theory and Coding
Information

Book description

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

Reviews

'William Shaw's Complex Analysis with Mathematica is a remarkable achievement. 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.'

Roger Penrose - University of Oxford

'This is an innovative text in which the basic ideas of complex analysis are skillfully interwoven with geometry, chaos and physics through the learning and repeated application of Mathematica. This text moves from complex numbers, quadratic and cubic equations through to the Schwarz-Christoffel transformation and four-dimensional physics, and at each stage promotes understanding through geometric intuition and reader participation. It should appeal to anyone with an interest in the geometric side of complex analysis.'

Alan F. Beardon - University of Cambridge

'This book provides an inspiring way to learn complex analysis thanks to the inclusion of many topics of current interest in the field as well as the integration of highly visual Mathematica routines throughout. The book is sure to excite students about the field.'

Bob Devaney - Boston University

'The book is far more than a standard course of complex analysis or a guide to Mathematica® tools.'

Source: EMS Newsletter

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Contents

Contents
References
Bibliograpy
V., Adamchik and M., Trott (1994). Solving the Quintic, poster and numerous web resources available at http://library.wolfram.com/examples/quintic/
L.V., Ahlfors (1953, 1979). Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. (First and Third ed.) McGraw-Hill.
J., D'Angelo (2002). Inequalities in Complex Analysis. Mathematical Monograph #28, Mathematical Assoication of America.
T.B., Bahder (1995). Mathematica for Scientists and Engineers. Addison-Wesley.
T.N., Bailey and R.J., Baston (ed.) (1990). Twistors in Mathematics and Physics. London Mathematical Society Lecture Note Series 16. Cambridge University Press.
H., Bateman (1904). The solution of partial differential equations by means of definite integrals. Proceedings of the London Mathematical Society, 1 (2), p. 451–8.
H., Bateman (1944). Partial Differential Equations of Mathematical Physics. Dover.
A.F., Beardon (1991). Iteration of Rational Functions. Springer Graduate Texts in Mathematics, no. 132. Springer.
R.P., Boas (1987). Invitation to Complex Analysis. Random House.
J.J., Bowman, T.B.A., Senior and P.L.E., Uslenghi (1987). Electromagnetic and Acoustic Scattering by Simple Shapes, revised edition. Hemisphere Publishing.
D.M., Burton (1995). Burton's History of Mathematics, An Introduction, 3rd edn. Wm. C. Brown Publishers.
G., Cardano (1993). The Great Art, or the Rules of Algebra, translated by Richard Witmer. Dover Reprint.
A., Cayley (1879). The Newton-Fourier imaginary problem. American Journal of Mathematics, 2, p. 97.
H., Cartan (1961). The elementary theory of analytic functions of one or several complex variables. The original French version is 1961. The english translation dating from 1963 is available as a 1995 Dover reprint, where the relevant discussion can be found on p. 126.
A.H.-D., Cheng, P., Sidauruk and Y., Abousleiman (1994). Approximate inversion of the Laplace transform. The Mathematica Journal, 4 (2), p. 76–82.
H.S.M., Coxeter (1964). Regular compound tessellations of the hyperbolic plane. Proceedings of the Royal Society, A278, p. 147-167.
H.S.M., Coxeter (1965). Non-Euclidean Geometry, 5th ed.. University of Toronto Press.
B., Davies and B., Martin (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal of Computational Physiscs, 33 (1), p. 1-32.
J.W., Dettman (1965). Applied Complex Variables, Dover reprint.
R.M., Dickau (1997). Compilation of iterative and list operations. The Mathematica Journal, 1 (1), p. 14–15.
T.A., Driscoll (1996). Algorithm 765: a MATLAB toolbox for Schwarz-Christoffel mapping. ACM Transactions on Mathematical Software, 22, p. 168-186.
T.A., Driscoll and L.N., Trefethen (2002). Schwarz-Chistoffel Mapping. Cambridge University Press.
L.P., Eisenhart (1911). A fundamental parametric representation of space curves, Annals of Mathematics (Ser II), XIII, p. 17-35.
L.P., Eisenhart (1912). Minimal surfaces in Euclidean four-spaces, American Journal of Mathematics, 34, p. 215-236.
A., Eydeland and H., Geman (1995). Asian options revisited: inverting the Laplace transform. RISK Magazine, March.
M., Field and M., Golubitsky (1992). Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature. Oxford University Press. (Chapter 4). See also the web site at http://nothung.math.uh.edu/~mike/
M.D., Finn and S.M., Cox (2001). Stokes flow in a mixer with changing geometry. Journal of Engineering Mathematics, 41, p. 75-99.
P.R., Garabedian (1966). Free boundary flows of a viscous liquid. Communications on pure and applied mathematics, XIX (4), p. 421-434.
H., Geman and M., Yor (1993). Bessel processes, Asian options, and perpetuities. Mathematical Finance, 3 (4), p. 349-375.
H., Geman and M., Yor (1996). Pricing and hedging double-barrier options: a probabilistic approach. Mathematical Finance, 6 (4), p. 365-378.
I.S., Gradshteyn and I.M., Ryzhik (1980). Tables of integrals, series and products, corrected and enlarged edition. Academic Press.
A., Gray (1993). Modern differential geometry of curves and surfaces. CRC Press.
T.W., Gray and J., Glynn (1991). Exploring Mathematics with Mathematica, Addison-Wesley.
Getting Started with Mathematica on (Windows, Macintosh, Linux etc.) Systems. Wolfram Research Mathematica Documentation Kit.
N.J., Hitchin (1982). Monopoles and geodesics. Communications in Mathematical Physics, 83, p. 579-602.
L.H., Howell and L.N., Trefethen (1990). A modified Schwarz-Christoffel transformation for elongated regions. SIAM Journal of Scientific and Statistical Computing, 11, p. 928-949.
R. R., Huilgol (1981). Relation of the conjugate harmonic functions to f HzL in cylindrical polar coordinates. Australian Mathematical Society Gazette, 8 (1), p. 23-25.
J.D., Jackson (1975). Classical Electrodynamics, Second edition. Wiley.
N., Kunitomo and M., Ikeda (1992). Pricing options with curved boundaries. Mathematical Finance, 2 (4), p. 275-297.
E.V., Laitone (1977). Relation of the conjugate harmonic functions to f HzL. The American Mathematical Monthly, 84 (4), p. 281–283. (Available on-line at JSTOR).
R., Legendre (1949). Solutions plus complète du problème Blasius. Comptes Rendus, 228, p. 2008-2010.
I.V., Lindell (1995). Methods for Electromagnetic Field Analysis.IEEE Press/Oxford University Press Series on Electromagnetic Wave Theory.
S., Levy (1993). Automatic generation of hyperbolic tilings. In The Visual Mind, M., Emmer (ed.), MIT Press.
S., Levy and T., Orloff (1990). Automatic Escher. The Mathematica Journal, 1 (1), p.34-35.
R., Maeder (1994). The Mathematica Programmer. AP Professional. 554 Complex Analysis with Mathematica
R., Maeder (1995). Function iteration and chaos. The Mathematica Journal, 5 (2), p. 28-40.
R., Maeder (1997). Programming in Mathematica. Third Edition. Addison Wesley.
L.J., Mason (1990). Sources and currents; relative cohomology and non-Hausdorff twistor space. In Further Advances in twistor theory Vol. I: The Penrose transform and its Applications. Pitman Research Notes in Mathematics 231. Longman.
L.J., Mason and L.P., Hughston (ed.) (1990). Further advances in twistor theory, Vol. 1: The Penrose transform and its Applications. Pitman Research Notes in Mathematics 231. Longman.
L.J., Mason, L.P., HughstonP.Z., and Kobak (ed.) (1990). Further advances in twistor theory, Vol. 2: Integrable systems, conformal geometry and gravitation. Pitman Research Notes in Mathematics 232. Longman.
Mathematica Applications Package - Dynamic Visualizer (1999). See the web site at: http://www.wolfram.com/products/applications/visualizer/
R., May (1976). Simple mathematical models with very complicated dynamics. Nature, 261, p. 459-469.
L.M., Milne-Thomson (1937). On the relation of an analytic function of z to its real and imaginary parts. Mathematical Gazette, 244 (21), p. 228–229.
L.M., Milne-Thomson (1938). Theoretical Hydrodynamics, first edition. See also second edition (1949), third Edition (1955), fourth Edition (1962). The fifth edition remains available as a Dover reprint.
M., Montcheuil (1905). Résolution de l'équation ds2 = dx2 + dy2 + dz2, Bulletin de la Société Mathématique de France, 33, p. 170-171.
T., Needham (1997). Visual Complex Analysis. Clarendon Press.
H., Ockendon and J.R., Ockendon (1995). Viscous Flow. Cambridge texts in applied mathematics, Cambridge University Press.
J.R., Ockendon, S.D., Howison, A., Lacey and A., Movchan (2003). Applied Partial Differential Equations, revised edition, Oxford University Press.
H-O., Peitgen and P.H., Richter (1986). The Beauty of Fractals: images of complex dynamical systems, Springer.
R., Penrose (1959). The apparent shape of a relativistically moving sphere. Proceedings of the Cambridge Philosophical Society, 55, p. 137–9.
R., Penrose (1999). The Emperor's New Mind.Oxford University Press.
R., Penrose (2004). The Road to Reality. Jonathan Cape.
R., Penrose and W., Rindler (1984a). Spinors and space-time, Vol. 1: Two-spinor calculus and relativistic fields. Cambridge University Press.
R., Penrose and W., Rindler (1984b). Spinors and space-time, Vol. 2: Spinor and twistor methods in space-time geometry. Cambridge University Press.
W.H., Press, S.A., Teukolsky, W. T., Vetterling and B.P., Flannery (1992). Numerical Recipes in C, The Art of Scientific Computing, Second Edition. Cambridge University Press.
A.P., Prudnikov, Yu.A., Brychkov and O.I., Marichev (1998). Integrals and Series, Vol 4: Direct Laplace Transforms, (second printing). Gordon and Breach.
A.P., Prudnikov, Yu.A., Brychkov and O.I., Marichev (2002). Integrals and Series, Vol 5: Inverse Laplace Transforms, (digital edition). Gordon and Breach.
K.B., Ranger (1991). A complex variable integration technique for the two-dimensional Navier-Stokes equations. Quarterly of Applied Mathematics, XLIX (2), p. 555-562.
K.B., Ranger (1994). Parametrization of general solutions for the Navier-Stokes equation., Quarterly of Applied Mathematics, LII, p. 335–41.
M., Rizzardi (1995). A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform. ACM Transactions on Mathematical Software, 21 (4), p. 347–371.
W., Rudin (1976). Principles of Mathematical Analysis. McGraw-Hill.
W.T., Shaw (1985). Twistors, minimal surfaces and strings, Classical and Quantum Gravity, 2, L113-119.
W.T., Shaw and J., Tigg (1993). Applied Mathematica. Addison-Wesley.
W.T., Shaw (1995). Symmetric chaos in the complex plane. The Mathematica Journal, 5(3), p. 85-89.
W.T., Shaw (1995b). MathLive and the virtual dynamics lab. The Mathematica Journal, 5 (2), p. 14-20.
W.T., Shaw (1998). Modelling Financial Derivatives with Mathematica, Cambridge University Press.
W.T., Shaw (2004). Recovering holomorphic unctions from their real or imaginary parts without the Cauchy-Riemann equations. SIAM Review, 46 (4), p. 717–728.
W.T., Shaw and L.P., Hughston (1990). Twistors and strings. In Twistors in mathematics and physics, eds. T.N., Bailey and R., Baston. London Mathematical Society Lecture Notes, no. 156. Cambridge University Press.
B.C., Skotton (1994). On amplitude and phase in printed characters. The Mathematica Journal, 4 (2), p. 83–86.
M.R., Spiegel (1965). Laplace Transforms. Schaum's Outlines series, McGraw-Hill.
M.R., Spiegel (1981). Theory and Problems of Complex Variables. Schaum's outline series, McGraw-Hill.
S., Stahl (1993). The Poincaré half-plane: a gateway to modern geometry. Jones and Bartlett.
R.A., Struble (1979). Obtaining analytic functions and conjugate harmonic functions. Quarterly of Applied Mathematics, 37 p. 79-81.
A., Talbot (1979). The accurate numerical inversion of Laplace transforms. Journal of the Institute of Mathematics and its Applications, 23, p. 97-120.
J., Terrell (1959). Invisibility of the Lorentz contraction, Physical Review D, 116 (4), p. 1041–5.
L.N., Trefethen (1980). Numerical computation of the Schwarz-Christoffel transformation. SIAM Journal of Scientific and Statistical Computing, 1, p. 82-102.
L.N., Trefethen (ed.) (1986). Numerical Conformal Mapping. North-Holland.
L.N., Trefethen and T.A., Driscoll (1998). Schwarz-Christoffel mapping in the computer era, Oxford University Computing Laboratory report 98/08.
J., Vecer (2002). Unified Asian pricing. RISK Magazine, June.
L.I., Volkovyskii, G.L., Lunts, I.G., Aramanovich (1960). (Russian original edition) A Collection of Problems on Complex Analysis. English translation (1965) Pergamon Press.
Currently available as Dover reprint (1991).
S., Wagon (1991). Mathematica in Action. W.H. Freeman.
R.S., Ward, R.S (1981). Axissymmetric stationary fields. In Twistor Newsletter 11.
Reprinted (1990) In Further Advances in twistor theory Vol. I: The Penrose transform and its Applications. Pitman Research Notes in Mathematics 231. Longman.
K., Weierstrass (1866a). Über die Flächen derren mittlere Krümmung überall gleich null ist. Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, p. 612-625.
K., Weierstrass (1866b). (1866a via the world-wide web): http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schri ften/anzeige/index_html?band=09-mon/1866&seite:int=628
E.T., Whittaker (1903). On the partial differential equations of mathematical physics. Mathematische Annalen, 57, p. 333-355.
E.T., Whittaker and G.N., Watson (1984). A course of modern analysis. Cambridge University Press.
T. Wickham, Jones (1994). Mathematica Graphics, Techniques and Applications. Springer.
S., Wolfram (2003). The Mathematica Book, 5th Edition. Wolfram Media.

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