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Many things, which are briefly described in others books, in remarks or exercises, are given in full detail … . [It] will please readers interested … in applications as well as those who want to know how things really work and prefer deeper and more detailed treatment of the material. The book also contains more than 200 examples and 150 exercises. … I recommend it for courses in complex function theory … and also as a reference book.
- EMS Newsletter, Dec. 2004
Many things, which are briefly described in others books, in remarks or exercises, are given in full detail … . [It] will please readers interested … in applications as well as those who want to know how things really work and prefer deeper and more detailed treatment of the material. The book also contains more than 200 examples and 150 exercises. … I recommend it for courses in complex function theory … and also as a reference book.
- EMS Newsletter, Dec. 2004
… [A]bundant examples and 'hints' to aid readers [are provided]. Summing Up: Recommended. Upper-division undergraduates through professionals.
- CHOICE, March 2005, Vol. 42, No. 07
… [A]bundant examples and hints to aid readers [are provided]. Summing Up: Recommended. Upper-division undergraduates through professionals.
- CHOICE, March 2005, Vol. 42, No. 07
Product Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
Many things, which are briefly described in others books, in remarks or exercises, are given in full detail … . [It] will please readers interested … in applications as well as those who want to know how things really work and prefer deeper and more detailed treatment of the material. The book also contains more than 200 examples and 150 exercises. … I recommend it for courses in complex function theory … and also as a reference book.
- EMS Newsletter, Dec. 2004
Many things, which are briefly described in others books, in remarks or exercises, are given in full detail … . [It] will please readers interested … in applications as well as those who want to know how things really work and prefer deeper and more detailed treatment of the material. The book also contains more than 200 examples and 150 exercises. … I recommend it for courses in complex function theory … and also as a reference book.
- EMS Newsletter, Dec. 2004
… [A]bundant examples and 'hints' to aid readers [are provided]. Summing Up: Recommended. Upper-division undergraduates through professionals.
- CHOICE, March 2005, Vol. 42, No. 07
… [A]bundant examples and hints to aid readers [are provided]. Summing Up: Recommended. Upper-division undergraduates through professionals.
- CHOICE, March 2005, Vol. 42, No. 07
Product Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
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Inside This Book
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First Sentence:
Mathematical analysis deals with the dependence of quantities (such as real numbers, vectors, points in Euclidean spares) on each other. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complex sine function, fundamental period parallelogram, complex differentiable, corresponding principal parts, complex differentiability, holornorphic function, disk centred, sigma function, residue calculus, power series representation, disk with radius, continuously differentiable mapping, prescribed zeros, holomorphic function, entire complex plane, mapping properties, complex exponential function, univalent functions, unit disk, meromorphic function, complex logarithm, removable singularity, entire function, elliptic function, rotates vectors Key Phrases - Capitalized Phrases (CAPs): (learn more)
Integral Theorem, Proof Let, Residue Theorem, Definition Let, Fundamental Theorem of Algebra, Proof Suppose, Maximum Modulus Principle, Hint Let, Cauchy Type Integral, Hint Using, Unique Continuation Theorem, Hint Apply, Hint Observe, Mapping Theorem, Maximum Minimum Principle, Division Algorithm, L'Hospital's Rule, Proof Choose, Maximum Principle, Definition Suppose, Fundamental Theorem of Calculus, Using Morera's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Mathematical analysis deals with the dependence of quantities (such as real numbers, vectors, points in Euclidean spares) on each other. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complex sine function, fundamental period parallelogram, complex differentiable, corresponding principal parts, complex differentiability, holornorphic function, disk centred, sigma function, residue calculus, power series representation, disk with radius, continuously differentiable mapping, prescribed zeros, holomorphic function, entire complex plane, mapping properties, complex exponential function, univalent functions, unit disk, meromorphic function, complex logarithm, removable singularity, entire function, elliptic function, rotates vectors Key Phrases - Capitalized Phrases (CAPs): (learn more)
Integral Theorem, Proof Let, Residue Theorem, Definition Let, Fundamental Theorem of Algebra, Proof Suppose, Maximum Modulus Principle, Hint Let, Cauchy Type Integral, Hint Using, Unique Continuation Theorem, Hint Apply, Hint Observe, Mapping Theorem, Maximum Minimum Principle, Division Algorithm, L'Hospital's Rule, Proof Choose, Maximum Principle, Definition Suppose, Fundamental Theorem of Calculus, Using Morera's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 15
books:
See all 15 books this book cites
- The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) by Benjamin Fine on page 195, and Back Matter
- Combinatorial Topology by P. S. Alexandrov in Back Matter
- Invitation to Complex Analysis (The Random House/Birkhauser mathematics series) by R. P. Boas in Back Matter
- Basic Complex Analysis by Jerrold E. Marsden in Back Matter
- Singular Integral Equations by N.I. Muskhelishvili in Back Matter
See all 15 books this book cites
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