{"product_id":"complex-analysis-the-argument-principle-in-analysis-and-topology-dover-books-on-mathematics","title":"Complex Analysis: The Argument Principle in Analysis and Topology (Dover Books on Mathematics)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tContents \n\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e Part I Angles \n\u003cp\u003e\u003c\/p\u003e Chapter 1 \n\u003cbr\u003e 1.1 Sets \n\u003cbr\u003e 1.2 Complex numbers \n\u003cbr\u003e 1.3 Upper bounds \n\u003cbr\u003e 1.4 Square roots \n\u003cbr\u003e 1.5 Distance \n\u003cp\u003e\u003c\/p\u003e Chapter 2 \n\u003cbr\u003e 2.1 Infinite series \n\u003cbr\u003e 2.2 Tests for convergence \n\u003cbr\u003e 2.3 The Cauchy project \n\u003cp\u003e\u003c\/p\u003e Chapter 3 \n\u003cbr\u003e 3.1 Continuity \n\u003cbr\u003e 3.2 Real continuous functions \n\u003cp\u003e\u003c\/p\u003e Chapter 4 \n\u003cbr\u003e 4.1 The exponential function \n\u003cbr\u003e 4.2 The trigonometric functions \n\u003cbr\u003e 4.3 Periodicity \n\u003cbr\u003e 4.4 The hyperbolic functions \n\u003cp\u003e\u003c\/p\u003e Chapter 5 \n\u003cbr\u003e 5.1 The argument of a complex number \n\u003cbr\u003e 5.2 Logarithms \n\u003cbr\u003e 5.3 Exponents \n\u003cbr\u003e 5.4 Continuity of the logarithm \n\u003cp\u003e\u003c\/p\u003e Part II Basic Complex Analysis \n\u003cp\u003e\u003c\/p\u003e Chapter 6 \n\u003cbr\u003e 6.1 Open and closed sets \n\u003cbr\u003e 6.2 Connected sets \n\u003cbr\u003e 6.3 Limits \n\u003cbr\u003e 6.4 Compact sets \n\u003cbr\u003e 6.5 Homeomorphisms \n\u003cbr\u003e 6.6 Uniform convergence \n\u003cp\u003e\u003c\/p\u003e Chapter 7 \n\u003cbr\u003e 7.1 Plane curves \n\u003cbr\u003e 7.2 The index of a curve \n\u003cbr\u003e 7.3 Properties of the index \n\u003cp\u003e\u003c\/p\u003e Chapter 8 \n\u003cbr\u003e 8.1 Polynomials \n\u003cbr\u003e 8.2 Power series \n\u003cbr\u003e 8.3 Analytic functions \n\u003cbr\u003e 8.4 Inequalities \n\u003cbr\u003e 8.5 The zeros of analytic functions \n\u003cp\u003e\u003c\/p\u003e Chapter 9 \n\u003cbr\u003e 9.1 Derivatives \n\u003cbr\u003e 9.2 Line integrals \n\u003cbr\u003e 9.3 Inequalities \n\u003cbr\u003e 9.4 Chains and cycles \n\u003cbr\u003e 9.5 Evaluation of integrals \n\u003cbr\u003e 9.6 Cauchy's Theorem \n\u003cbr\u003e 9.7 Applications \n\u003cp\u003e\u003c\/p\u003e Chapter 10 \n\u003cbr\u003e 10.1 Conformal mapping \n\u003cbr\u003e 10.2 Stereographic projection \n\u003cbr\u003e 103. Mobius transformations \n\u003cp\u003e\u003c\/p\u003e Part III Interactions with Plane Topology \n\u003cp\u003e\u003c\/p\u003e Chapter 11 \n\u003cbr\u003e 11.1 Simply connected domains \n\u003cbr\u003e 11.2 The Riemann Mapping Theorem \n\u003cbr\u003e 11.3 Branches of the argument \n\u003cbr\u003e 11.4 The Jordan Curve Theorem \n\u003cbr\u003e 11.5 Conformal mapping of a Jordan domain \n\u003cp\u003e\u003c\/p\u003e Appendix \n\u003cbr\u003e Bibliography \n\u003cbr\u003e Index\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eBiographical Note\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tAlan F. Beardon received his PhD from the University of London in 1964 and was Professor of Mathematics at the University of Cambridge from 1970 until he became Emeritus in 2007. His many books include \n\u003ci\u003eA Primer on Riemann Surfaces, The Geometry of Discrete Groups, \u003c\/i\u003eand \n\u003ci\u003eLimits: A New Approach to Real Analysis.\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eBrief Description\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tOriginally published: New York: Wiley, 1979; with an update for theorem 5.4.1, provided by author.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tWith its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insights by covering angles, basic complex analysis, and interactions with plane topology while focusing on the concepts of angle and winding numbers. \n\u003cbr\u003e Part I takes a critical look at the concept of an angle, illustrating that because a nonzero complex number varies continuously, one may select a continuously changing value of its argument. Part II builds upon this material, using the argument and its continuous variation as a tool in further studies and clarifying the complementary aspects of complex analysis and plane topology. Part III explores the link between the two subjects to their mutual benefit. The first two sections are intended for advanced undergraduates and graduate students in mathematics and contain sufficient material for a single course. The final section is geared toward the complex analyst and is intended to provide a foundation for further study.\u003cbr\u003e\u003cbr\u003e\n\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46581131608195,"sku":"SPTM-9780486837185","price":22.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486837185_spiral_a7ba3312-8bc1-490d-98e3-b5dc7fac578f.png?v=1770802785","url":"https:\/\/sebink.com\/products\/complex-analysis-the-argument-principle-in-analysis-and-topology-dover-books-on-mathematics","provider":"Sebink","version":"1.0","type":"link"}