An Introduction to Complex Analysis [electronic resource] / by Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas. - 1. - XIV, 331 p. online resource.

Preface.-Complex Numbers.-Complex Numbers II -- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I -- Elementary Functions II -- Mappings by Functions -- Mappings by Functions II -- Curves, Contours, and Simply Connected Domains -- Complex Integration -- Independence of Path -- Cauchy–Goursat Theorem -- Deformation Theorem -- Cauchy’s Integral Formula -- Cauchy’s Integral Formula for Derivatives -- Fundamental Theorem of Algebra -- Maximum Modulus Principle -- Sequences and Series of Numbers -- Sequences and Series of Functions -- Power Series -- Taylor’s Series -- Laurent’s Series -- Zeros of Analytic Functions -- Analytic Continuation -- Symmetry and Reflection -- Singularities and Poles I -- Singularities and Poles II -- Cauchy’s Residue Theorem -- Evaluation of Real Integrals by Contour Integration I -- Evaluation of Real Integrals by Contour Integration II -- Indented Contour Integrals -- Contour Integrals Involving Multi–valued Functions -- Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems -- Behavior of Analytic Mappings -- Conformal Mappings -- Harmonic Functions -- The Schwarz–Christoffel Transformation -- Infinite Products -- Weierstrass’s Factorization Theorem -- Mittag–Leffler’s Theorem -- Periodic Functions -- The Riemann Zeta Function -- Bieberbach’s Conjecture -- The Riemann Surface -- Julia and Mandelbrot Sets -- History of Complex Numbers -- References for Further Reading -- Index.

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples to drive the presentation -Includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section -covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics -Provides a concise history of complex numbers An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

9781461401957

10.1007/978-1-4614-0195-7 doi

Mathematics.

Mathematical analysis.

Analysis (Mathematics).

Functions of complex variables.

Mathematics.

Functions of a Complex Variable.

Analysis.

QA331-355

515.9