Real and Complex Analysis

Real and Complex Analysis

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Presents Real & Complex Analysis Together Using a Unified Approach A two-semester course in analysis at the advanced undergraduate or first-year graduate level Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA's 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book's website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks-one for real function theory and one for complex function more

Product details

  • Hardback | 567 pages
  • 154.94 x 231.14 x 30.48mm | 907.18g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 67 black & white illustrations
  • 1584888067
  • 9781584888062
  • 1,581,770

About Christopher Apelian

Christopher Apelian is an associate professor and chair of the Department of Mathematics and Computer Science at Drew University. Dr. Apelian has published papers on the application of probability and stochastic processes to the modeling of turbulent transport. Steve Surace is an associate professor in the Department of Mathematics and Computer Science at Drew University. Dr. Surace is also the Associate Director of the New Jersey Governor's School in the Sciences held at Drew University every more

Table of contents

The Spaces R, Rk, and C The Real Numbers R The Real Spaces Rk The Complex Numbers C Point-Set Topology Bounded Sets Classification of Points Open and Closed Sets Nested Intervals and the Bolzano-Weierstrass Theorem Compactness and Connectedness Limits and Convergence Definitions and First Properties Convergence Results for Sequences Topological Results for Sequences Properties of Infinite Series Manipulations of Series in R Functions: Definitions and Limits Definitions Functions as Mappings Some Elementary Complex Functions Limits of Functions Functions: Continuity and Convergence Continuity Uniform Continuity Sequences and Series of Functions The Derivative The Derivative for f: D1 --> R The Derivative for f: Dk --> R The Derivative for f: Dk --> Rp The Derivative for f: D --> C The Inverse and Implicit Function Theorems Real Integration The Integral of f: [a, b] --> R Properties of the Riemann Integral Further Development of Integration Theory Vector-Valued and Line Integrals Complex Integration Introduction to Complex Integrals Further Development of Complex Line Integrals Cauchy's Integral Theorem and Its Consequences Cauchy's Integral Formula Further Properties of Complex Differentiable Functions Appendices: Winding Numbers Revisited Taylor Series, Laurent Series, and the Residue Calculus Power Series Taylor Series Analytic Functions Laurent's Theorem for Complex Functions Singularities The Residue Calculus Complex Functions as Mappings The Extended Complex Plane Lineal Fractional Transformations Conformal Mappings Bibliography Index Exercises appear at the end of each more

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