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Introduction to Complex Analysis
About this Title
Michael E. Taylor, University of North Carolina, Chapel Hill, NC
Publication: Graduate Studies in Mathematics
Publication Year:
2019; Volume 202
ISBNs: 978-1-4704-5286-5 (print); 978-1-4704-5448-7 (online)
DOI: https://doi.org/10.1090/gsm/202
MathSciNet review: MR3969984
MSC: Primary 30-01
ReadershipTable of Contents
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Front/Back Matter
Chapters
- Basic calculus in the complex domain
- Going deeper – the Cauchy integral theorem and consequences
- Fourier analysis complex function theory
- Residue calculus, the argument principle, and two very special functions
- Conformal maps and geometrical aspects of complex function theory
- Elliptic functions and elliptic integrals
- Complex analysis and differential equations
- Mark J. Ablowitz and Athanassios S. Fokas, Complex variables: introduction and applications, 2nd ed., Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2003. MR 1989049, DOI 10.1017/CBO9780511791246
- Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
- R. Andriambololoma, H. Rakotoson, R. Gilbert, and R. Tokiniaina, Method to reduce quintic equations using linear algebra, HEP-MAD 09, Aniananarivo (Madagascar), 21-28th Aug., 2009.
- Tom M. Apostol, Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976. MR 0434929
- W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York, 1964. MR 0185155
- Joseph Bak and Donald J. Newman, Complex analysis, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1982. MR 671250
- Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1987. A study in analytic number theory and computational complexity; A Wiley-Interscience Publication. MR 877728
- Lennart Carleson and Theodore W. Gamelin, Complex dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1230383, DOI 10.1007/978-1-4612-4364-9
- C. Herbert Clemens, A scrapbook of complex curve theory, University Series in Mathematics, Plenum Press, New York-London, 1980. MR 614289
- John B. Conway, Functions of one complex variable, 2nd ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978. MR 503901
- William F. Donoghue Jr., Distributions and Fourier transforms, Pure and Applied Mathematics, vol. 32, Academic Press, New York, 1969. MR 3363413
- H. M. Edwards, Riemann’s zeta function, Dover Publications, Inc., Mineola, NY, 2001. Reprint of the 1974 original [Academic Press, New York; MR0466039 (57 #5922)]. MR 1854455
- Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
- Otto Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York-Berlin, 1981. Translated from the German by Bruce Gilligan. MR 648106
- Theodore W. Gamelin, Complex analysis, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2001. MR 1830078, DOI 10.1007/978-0-387-21607-2
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- Marvin J. Greenberg, Lectures on algebraic topology, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0215295
- Robert E. Greene and Steven G. Krantz, Function theory of one complex variable, 3rd ed., Graduate Studies in Mathematics, vol. 40, American Mathematical Society, Providence, RI, 2006. MR 2215872, DOI 10.1090/gsm/040
- E. Hille, Analytic Function Theory, Vols. 1–2, Chelsea, New York, 1962.
- E. Hille, Ordinary Differential Equations in the Complex Plane, Wiley-Interscience, New York, 1976.
- R. Bruce King, Beyond the quartic equation, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1401346
- Felix Klein, Lectures on the icosahedron and the solution of equations of the fifth degree, Second and revised edition, Dover Publications, Inc., New York, N.Y., 1956. Translated into English by George Gavin Morrice. MR 0080930
- Steven G. Krantz, Complex analysis: the geometric viewpoint, Carus Mathematical Monographs, vol. 23, Mathematical Association of America, Washington, DC, 1990. MR 1074176
- Steven G. Krantz, Function theory of several complex variables, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. MR 635928
- Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
- Derek F. Lawden, Elliptic functions and applications, Applied Mathematical Sciences, vol. 80, Springer-Verlag, New York, 1989. MR 1007595, DOI 10.1007/978-1-4757-3980-0
- N. N. Lebedev, Special functions and their applications, Dover Publications, Inc., New York, 1972. Revised edition, translated from the Russian and edited by Richard A. Silverman; Unabridged and corrected republication. MR 0350075
- Rafe Mazzeo and Michael Taylor, Curvature and uniformization, Israel J. Math. 130 (2002), 323–346. MR 1919383, DOI 10.1007/BF02764082
- Henry McKean and Victor Moll, Elliptic curves, Cambridge University Press, Cambridge, 1997. Function theory, geometry, arithmetic. MR 1471703, DOI 10.1017/CBO9781139174879
- John Milnor, Dynamics in one complex variable, Friedr. Vieweg & Sohn, Braunschweig, 1999. Introductory lectures. MR 1721240
- James R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. MR 0464128
- Zeev Nehari, Conformal mapping, Dover Publications, Inc., New York, 1975. Reprinting of the 1952 edition. MR 0377031
- D. J. Newman, Simple analytic proof of the prime number theorem, Amer. Math. Monthly 87 (1980), no. 9, 693–696. MR 602825, DOI 10.2307/2321853
- Ivan Niven, A simple proof that $\pi$ is irrational, Bull. Amer. Math. Soc. 53 (1947), 509. MR 21013, DOI 10.1090/S0002-9904-1947-08821-2
- F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0435697
- S. J. Patterson, Eisenstein and the quintic equation, Historia Math. 17 (1990), no. 2, 132–140 (English, with French and German summaries). MR 1057021, DOI 10.1016/0315-0860(90)90049-J
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210528
- Donald Sarason, Complex function theory, 2nd ed., American Mathematical Society, Providence, RI, 2007. MR 2368077, DOI 10.1090/mbk/049
- Joel L. Schiff, Normal families, Universitext, Springer-Verlag, New York, 1993. MR 1211641, DOI 10.1007/978-1-4612-0907-2
- Barry Simon, Basic complex analysis, A Comprehensive Course in Analysis, Part 2A, American Mathematical Society, Providence, RI, 2015. MR 3443339, DOI 10.1090/simon/002.1
- Barry Simon, Advanced complex analysis, A Comprehensive Course in Analysis, Part 2B, American Mathematical Society, Providence, RI, 2015. MR 3364090, DOI 10.1090/simon/002.2
- Michael Spivak, A comprehensive introduction to differential geometry. Vol. V, Publish or Perish, Inc., Boston, Mass., 1975. MR 0394453
- Joseph L. Taylor, Complex variables, Pure and Applied Undergraduate Texts, vol. 16, American Mathematical Society, Providence, RI, 2011. MR 2839384
- M. Taylor, Introduction to Analysis in One Variable, Preprint, 2019.
- M. Taylor, Introduction to Analysis in Several Variables, Preprint, 2019.
- Michael E. Taylor, Partial differential equations, Texts in Applied Mathematics, vol. 23, Springer-Verlag, New York, 1996. Basic theory. MR 1395147, DOI 10.1007/978-1-4684-9320-7
- Michael E. Taylor, Measure theory and integration, Graduate Studies in Mathematics, vol. 76, American Mathematical Society, Providence, RI, 2006. MR 2245472, DOI 10.1090/gsm/076
- M. Taylor, Introduction to Differential Equations, American Math. Soc., Providence RI, 2011.
- M. Taylor, Linear Algebra, Preprint, 2019.
- M. Tsuji, Potential theory in modern function theory, Chelsea Publishing Co., New York, 1975. Reprinting of the 1959 original. MR 0414898
- H. Umemura, Resolution of algebraic equations by theta constants, pp. 261–270 in Tata Lectures on Theta II (D. Mumford), Birkhauser, Boston, 2007.
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
- E. Whittaker and G. Watson, Modern Analysis (4th ed.), Cambridge Univ. Press, Cambridge UK, 1927.