{"product_id":"complex-analysis-isbn-9781118705223","title":"Complex Analysis","description":"\u003cp\u003e\u003cb\u003eA thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWritten with a reader-friendly approach, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory \u003c\/i\u003efeatures 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.\u003c\/p\u003e \u003cp\u003eThoroughly classroom tested at multiple universities, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory \u003c\/i\u003efeatures:\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePlentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects\u003c\/li\u003e \u003cli\u003eNumerous figures to illustrate geometric concepts and constructions used in proofs\u003c\/li\u003e \u003cli\u003eRemarks 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\u003c\/li\u003e \u003cli\u003eAppendices on the basics of sets and functions and a handful of useful results from advanced calculus\u003c\/li\u003e \u003c\/ul\u003e Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory \u003c\/i\u003eis 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 the beautiful subject of complex analysis.\u003cbr\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The Complex Numbers 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Why? 1\u003c\/p\u003e \u003cp\u003e1.2 The Algebra of Complex Numbers 3\u003c\/p\u003e \u003cp\u003e1.3 The Geometry of the Complex Plane 7\u003c\/p\u003e \u003cp\u003e1.4 The Topology of the Complex Plane 9\u003c\/p\u003e \u003cp\u003e1.5 The Extended Complex Plane 16\u003c\/p\u003e \u003cp\u003e1.6 Complex Sequences 18\u003c\/p\u003e \u003cp\u003e1.7 Complex Series 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Complex Functions and Mappings 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Continuous Functions 29\u003c\/p\u003e \u003cp\u003e2.2 Uniform Convergence 34\u003c\/p\u003e \u003cp\u003e2.3 Power Series 38\u003c\/p\u003e \u003cp\u003e2.4 Elementary Functions and Euler’s Formula 43\u003c\/p\u003e \u003cp\u003e2.5 Continuous Functions as Mappings 50\u003c\/p\u003e \u003cp\u003e2.6 Linear Fractional Transformations 53\u003c\/p\u003e \u003cp\u003e2.7 Derivatives 64\u003c\/p\u003e \u003cp\u003e2.8 The Calculus of Real Variable Functions 70\u003c\/p\u003e \u003cp\u003e2.9 Contour Integrals 75\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Analytic Functions 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Principle of Analyticity 87\u003c\/p\u003e \u003cp\u003e3.2 Differentiable Functions are Analytic 89\u003c\/p\u003e \u003cp\u003e3.3 Consequences of Goursat’s Theorem 100\u003c\/p\u003e \u003cp\u003e3.4 The Zeros of Analytic Functions 104\u003c\/p\u003e \u003cp\u003e3.5 The Open Mapping Theorem and Maximum Principle 108\u003c\/p\u003e \u003cp\u003e3.6 The Cauchy–Riemann Equations 113\u003c\/p\u003e \u003cp\u003e3.7 Conformal Mapping and Local Univalence 117\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Cauchy’s Integral Theory 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Index of a Closed Contour 127\u003c\/p\u003e \u003cp\u003e4.2 The Cauchy Integral Formula 133\u003c\/p\u003e \u003cp\u003e4.3 Cauchy’s Theorem 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Residue Theorem 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Laurent Series 145\u003c\/p\u003e \u003cp\u003e5.2 Classification of Singularities 152\u003c\/p\u003e \u003cp\u003e5.3 Residues 158\u003c\/p\u003e \u003cp\u003e5.4 Evaluation of Real Integrals 165\u003c\/p\u003e \u003cp\u003e5.5 The Laplace Transform 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Harmonic Functions and Fourier Series 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Harmonic Functions 183\u003c\/p\u003e \u003cp\u003e6.2 The Poisson Integral Formula 191\u003c\/p\u003e \u003cp\u003e6.3 Further Connections to Analytic Functions 201\u003c\/p\u003e \u003cp\u003e6.4 Fourier Series 210\u003c\/p\u003e \u003cp\u003eEpilogue 227\u003c\/p\u003e \u003cp\u003eA Sets and Functions 239\u003c\/p\u003e \u003cp\u003eB Topics from Advanced Calculus 247\u003c\/p\u003e \u003cp\u003eReferences 255\u003c\/p\u003e \u003cp\u003eIndex 257\u003c\/p\u003e \u003cp\u003e\"The textbook is appropriate for students and can serve as a key reference for anyone interested in learning or reviewing the theory of complex functions of a complex variable.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2016)\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eJerry R. Muir, Jr., PhD,\u003c\/b\u003e is Professor of Mathematics at The University of Scranton. He has authored over one dozen research articles in complex-flavored analysis, primarily on geometric function theory in several complex variables.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eA thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eWritten with a reader-friendly approach, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eThoroughly classroom tested at multiple universities, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory\u003c\/i\u003e features: \u003c\/p\u003e\u003cul\u003e \u003cli\u003ePlentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects\u003c\/li\u003e \u003cli\u003eNumerous figures to illustrate geometric concepts and constructions used in proofs\u003c\/li\u003e \u003cli\u003eRemarks 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\u003c\/li\u003e \u003cli\u003eAppendices on the basics of sets and functions and a handful of useful results from advanced calculus\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAppropriate for students majoring in pure or applied mathematics as well as physics or engineering, \u003ci\u003eComplex Analysis: A Modern First Course in Function Theory\u003c\/i\u003e 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 the beautiful subject of complex analysis.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988959215845,"sku":"NP9781118705223","price":82.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118705223.jpg?v=1761782213","url":"https:\/\/k12savings.com\/es\/products\/complex-analysis-isbn-9781118705223","provider":"K12savings","version":"1.0","type":"link"}