05312oam 22005293 450 991079581600332120220831094644.09781118705278(electronic bk.)9781118705223(MiAaPQ)EBC1895551(Au-PeEL)EBL1895551(CaPaEBR)ebr11078102(CaONFJC)MIL785546(OCoLC)890377891(EXLCZ)991769304720004120220831d2015 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierComplex Analysis A Modern First Course in Function Theory1st ed.New York :John Wiley & Sons, Incorporated,2015.©2015.1 online resource (277 pages)Print version: Muir, Jerry R. Complex Analysis New York : John Wiley & Sons, Incorporated,c2015 9781118705223 Intro -- Title Page -- Copyright -- Table of Contents -- Dedication -- Preface -- Chapter 1: The Complex Numbers -- 1.1 Why? -- 1.2 The Algebra of Complex Numbers -- 1.3 The Geometry of the Complex Plane -- 1.4 The Topology of the Complex Plane -- 1.5 The Extended Complex Plane -- 1.6 Complex Sequences -- 1.7 Complex Series -- Chapter 2: Complex Functions and Mappings -- 2.1 Continuous Functions -- 2.2 Uniform Convergence -- 2.3 Power Series -- 2.4 Elementary Functions and Euler's Formula -- 2.5 Continuous Functions as Mappings -- 2.6 Linear Fractional Transformations -- 2.7 Derivatives -- 2.8 The Calculus of Real-Variable Functions -- 2.9 Contour Integrals -- Chapter 3: Analytic Functions -- 3.1 The Principle of Analyticity -- 3.2 Differentiable Functions are Analytic -- 3.3 Consequences of Goursat's Theorem -- 3.4 The Zeros of Analytic Functions -- 3.5 The Open Mapping Theorem and Maximum Principle -- 3.6 The Cauchy-Riemann Equations -- 3.7 Conformal Mapping and Local Univalence -- Chapter 4: Cauchy's Integral Theory -- 4.1 The Index of a Closed Contour -- 4.2 The Cauchy Integral Formula -- 4.3 Cauchy's Theorem -- Chapter 5: The Residue Theorem -- 5.1 Laurent Series -- 5.2 Classification of Singularities -- 5.3 Residues -- 5.4 Evaluation of Real Integrals -- 5.5 The Laplace Transform -- Chapter 6: Harmonic Functions and Fourier Series -- 6.1 Harmonic Functions -- 6.2 The Poisson Integral Formula -- 6.3 Further Connections to Analytic Functions -- 6.4 Fourier Series -- Epilogue -- Local Uniform Convergence -- Harnack's Theorem -- Results for Simply Connected Domains -- The Riemann Mapping Theorem -- Appendix A: Sets and Functions -- Sets and Elements -- Functions -- Appendix B: Topics from Advanced Calculus -- The Supremum and Infimum -- Uniform Continuity -- The Cauchy Product -- Leibniz's Rule -- References -- Index.End User License Agreement.A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing thebeautiful subject of complex analysis.Geometric function theoryGeometryNumbers, ComplexElectronic books.Geometric function theory.Geometry.Numbers, Complex.515Muir Jerry R1541537Muir Jerry R., Jr1541538MiAaPQMiAaPQMiAaPQ9910795816003321Complex Analysis3793791UNINA