A Guide to Complex Variables /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | Dolciani mathematical expositions.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Title from publishers bibliographic system (viewed on 30 Jan 2012). |
| Beschreibung: | 1 online resource |
| ISBN: | 9780883859148 0883859149 |
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| 505 | 0 | |a A Guide to Complex Variables -- Preface -- Contents -- 1 The Complex Plane -- 1.1 Complex Arithmetic -- 1.1.1 The Real Numbers -- 1.1.2 The Complex Numbers -- 1.1.3 Complex Conjugate -- 1.1.4 Modulus of a Complex Number -- 1.1.5 The Topology of the Complex Plane -- 1.1.6 The Complex Numbers as a Field -- 1.1.7 The Fundamental Theorem of Algebra -- 1.2 The Exponential and Applications -- 1.2.1 The Exponential Function -- 1.2.2 The Exponential Using Power Series -- 1.2.3 Laws of Exponentiation -- 1.2.4 Polar Form of a Complex Number | |
| 505 | 8 | |a 1.2.5 Roots of Complex Numbers1.2.6 The Argument of a Complex Number -- 1.2.7 Fundamental Inequalities -- 1.3 Holomorphic Functions -- 1.3.1 Continuously Differentiable and Ck Functions -- 1.3.2 The Cauchy-Riemann Equations -- 1.3.3 Derivatives -- 1.3.4 Definition of Holomorphic Function -- 1.3.5 The Complex Derivative -- 1.3.6 Alternative Terminology for Holomorphic Functions -- 1.4 Holomorphic and Harmonic Functions -- 1.4.1 Harmonic Functions -- 1.4.2 How They are Related -- 2 Complex Line Integrals -- 2.1 Real and Complex Line Integrals -- 2.1.1 Curves | |
| 505 | 8 | |a 2.1.2 Closed Curves2.1.3 Differentiable and C^k Curves -- 2.1.4 Integrals on Curves -- 2.1.5 The Fundamental Theorem of Calculus along Curves -- 2.1.6 The Complex Line Integral -- 2.1.7 Properties of Integrals -- 2.2 Complex Differentiabilityand Conformality -- 2.2.1 Limits -- 2.2.2 Holomorphicity and the Complex Derivative -- 2.2.3 Conformality -- 2.3 The Cauchy Integral Formula and Theorem -- 2.3.1 The Cauchy Integral Theorem, Basic Form -- 2.3.2 The Cauchy Integral Formula -- 2.3.3 More General Forms of the Cauchy Theorems -- 2.3.4 Deformability of Curves | |
| 505 | 8 | |a 2.4 A Coda on the Limitations of The Cauchy Integral Formula3 Applications of the Cauchy Theory -- 3.1 The Derivatives of a Holomorphic Function -- 3.1.1 A Formula for the Derivative -- 3.1.2 The Cauchy Estimates -- 3.1.3 Entire Functions and Liouville�s Theorem -- 3.1.4 The Fundamental Theorem of Algebra -- 3.1.5 Sequences of Holomorphic Functions and their Derivatives -- 3.1.6 The Power Series Representation of a Holomorphic Function -- 3.2 The Zeros of a Holomorphic Function -- 3.2.1 The Zero Set of a Holomorphic Function | |
| 505 | 8 | |a 3.2.2 Discreteness of the Zeros of a Holomorphic Function3.2.3 Discrete Sets and Zero Sets -- 3.2.4 Uniqueness of Analytic Continuation -- 4 Isolated Singularities and Laurent Series -- 4.1 The Behavior of a Holomorphic Function near an Isolated Singularity -- 4.1.1 Isolated Singularities -- 4.1.2 A Holomorphic Function on a Punctured Domain -- 4.1.3 Classification of Singularities -- 4.1.4 Removable Singularities, Poles, and Essential Singularities -- 4.1.5 The Riemann Removable Singularities Theorem -- 4.1.6 The Casorati-Weierstrass Theorem | |
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| author | Krantz, Steven G. (Steven George), 1951- |
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| contents | A Guide to Complex Variables -- Preface -- Contents -- 1 The Complex Plane -- 1.1 Complex Arithmetic -- 1.1.1 The Real Numbers -- 1.1.2 The Complex Numbers -- 1.1.3 Complex Conjugate -- 1.1.4 Modulus of a Complex Number -- 1.1.5 The Topology of the Complex Plane -- 1.1.6 The Complex Numbers as a Field -- 1.1.7 The Fundamental Theorem of Algebra -- 1.2 The Exponential and Applications -- 1.2.1 The Exponential Function -- 1.2.2 The Exponential Using Power Series -- 1.2.3 Laws of Exponentiation -- 1.2.4 Polar Form of a Complex Number 1.2.5 Roots of Complex Numbers1.2.6 The Argument of a Complex Number -- 1.2.7 Fundamental Inequalities -- 1.3 Holomorphic Functions -- 1.3.1 Continuously Differentiable and Ck Functions -- 1.3.2 The Cauchy-Riemann Equations -- 1.3.3 Derivatives -- 1.3.4 Definition of Holomorphic Function -- 1.3.5 The Complex Derivative -- 1.3.6 Alternative Terminology for Holomorphic Functions -- 1.4 Holomorphic and Harmonic Functions -- 1.4.1 Harmonic Functions -- 1.4.2 How They are Related -- 2 Complex Line Integrals -- 2.1 Real and Complex Line Integrals -- 2.1.1 Curves 2.1.2 Closed Curves2.1.3 Differentiable and C^k Curves -- 2.1.4 Integrals on Curves -- 2.1.5 The Fundamental Theorem of Calculus along Curves -- 2.1.6 The Complex Line Integral -- 2.1.7 Properties of Integrals -- 2.2 Complex Differentiabilityand Conformality -- 2.2.1 Limits -- 2.2.2 Holomorphicity and the Complex Derivative -- 2.2.3 Conformality -- 2.3 The Cauchy Integral Formula and Theorem -- 2.3.1 The Cauchy Integral Theorem, Basic Form -- 2.3.2 The Cauchy Integral Formula -- 2.3.3 More General Forms of the Cauchy Theorems -- 2.3.4 Deformability of Curves 2.4 A Coda on the Limitations of The Cauchy Integral Formula3 Applications of the Cauchy Theory -- 3.1 The Derivatives of a Holomorphic Function -- 3.1.1 A Formula for the Derivative -- 3.1.2 The Cauchy Estimates -- 3.1.3 Entire Functions and Liouville�s Theorem -- 3.1.4 The Fundamental Theorem of Algebra -- 3.1.5 Sequences of Holomorphic Functions and their Derivatives -- 3.1.6 The Power Series Representation of a Holomorphic Function -- 3.2 The Zeros of a Holomorphic Function -- 3.2.1 The Zero Set of a Holomorphic Function 3.2.2 Discreteness of the Zeros of a Holomorphic Function3.2.3 Discrete Sets and Zero Sets -- 3.2.4 Uniqueness of Analytic Continuation -- 4 Isolated Singularities and Laurent Series -- 4.1 The Behavior of a Holomorphic Function near an Isolated Singularity -- 4.1.1 Isolated Singularities -- 4.1.2 A Holomorphic Function on a Punctured Domain -- 4.1.3 Classification of Singularities -- 4.1.4 Removable Singularities, Poles, and Essential Singularities -- 4.1.5 The Riemann Removable Singularities Theorem -- 4.1.6 The Casorati-Weierstrass Theorem |
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| series | Dolciani mathematical expositions. |
| series2 | Dolciani Mathematical Expositions ; |
| spelling | Krantz, Steven G. (Steven George), 1951- https://id.oclc.org/worldcat/entity/E39PBJw8VQ7cxG48KCfPym3RKd http://id.loc.gov/authorities/names/n81051364 A Guide to Complex Variables / Steven G. Krantz. Cambridge : Cambridge University Press, 2012. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Dolciani Mathematical Expositions ; v. 32 Title from publishers bibliographic system (viewed on 30 Jan 2012). A Guide to Complex Variables -- Preface -- Contents -- 1 The Complex Plane -- 1.1 Complex Arithmetic -- 1.1.1 The Real Numbers -- 1.1.2 The Complex Numbers -- 1.1.3 Complex Conjugate -- 1.1.4 Modulus of a Complex Number -- 1.1.5 The Topology of the Complex Plane -- 1.1.6 The Complex Numbers as a Field -- 1.1.7 The Fundamental Theorem of Algebra -- 1.2 The Exponential and Applications -- 1.2.1 The Exponential Function -- 1.2.2 The Exponential Using Power Series -- 1.2.3 Laws of Exponentiation -- 1.2.4 Polar Form of a Complex Number 1.2.5 Roots of Complex Numbers1.2.6 The Argument of a Complex Number -- 1.2.7 Fundamental Inequalities -- 1.3 Holomorphic Functions -- 1.3.1 Continuously Differentiable and Ck Functions -- 1.3.2 The Cauchy-Riemann Equations -- 1.3.3 Derivatives -- 1.3.4 Definition of Holomorphic Function -- 1.3.5 The Complex Derivative -- 1.3.6 Alternative Terminology for Holomorphic Functions -- 1.4 Holomorphic and Harmonic Functions -- 1.4.1 Harmonic Functions -- 1.4.2 How They are Related -- 2 Complex Line Integrals -- 2.1 Real and Complex Line Integrals -- 2.1.1 Curves 2.1.2 Closed Curves2.1.3 Differentiable and C^k Curves -- 2.1.4 Integrals on Curves -- 2.1.5 The Fundamental Theorem of Calculus along Curves -- 2.1.6 The Complex Line Integral -- 2.1.7 Properties of Integrals -- 2.2 Complex Differentiabilityand Conformality -- 2.2.1 Limits -- 2.2.2 Holomorphicity and the Complex Derivative -- 2.2.3 Conformality -- 2.3 The Cauchy Integral Formula and Theorem -- 2.3.1 The Cauchy Integral Theorem, Basic Form -- 2.3.2 The Cauchy Integral Formula -- 2.3.3 More General Forms of the Cauchy Theorems -- 2.3.4 Deformability of Curves 2.4 A Coda on the Limitations of The Cauchy Integral Formula3 Applications of the Cauchy Theory -- 3.1 The Derivatives of a Holomorphic Function -- 3.1.1 A Formula for the Derivative -- 3.1.2 The Cauchy Estimates -- 3.1.3 Entire Functions and Liouvilleâ€?s Theorem -- 3.1.4 The Fundamental Theorem of Algebra -- 3.1.5 Sequences of Holomorphic Functions and their Derivatives -- 3.1.6 The Power Series Representation of a Holomorphic Function -- 3.2 The Zeros of a Holomorphic Function -- 3.2.1 The Zero Set of a Holomorphic Function 3.2.2 Discreteness of the Zeros of a Holomorphic Function3.2.3 Discrete Sets and Zero Sets -- 3.2.4 Uniqueness of Analytic Continuation -- 4 Isolated Singularities and Laurent Series -- 4.1 The Behavior of a Holomorphic Function near an Isolated Singularity -- 4.1.1 Isolated Singularities -- 4.1.2 A Holomorphic Function on a Punctured Domain -- 4.1.3 Classification of Singularities -- 4.1.4 Removable Singularities, Poles, and Essential Singularities -- 4.1.5 The Riemann Removable Singularities Theorem -- 4.1.6 The Casorati-Weierstrass Theorem Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Fonctions d'une variable complexe. MATHEMATICS Complex Analysis. bisacsh Functions of complex variables fast Print version: Krantz, Steven G. Guide to Complex Variables. Washington : Mathematical Association of America, ©2014 9780883853382 Dolciani mathematical expositions. http://id.loc.gov/authorities/names/n42009859 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450270 Volltext |
| spellingShingle | Krantz, Steven G. (Steven George), 1951- A Guide to Complex Variables / Dolciani mathematical expositions. A Guide to Complex Variables -- Preface -- Contents -- 1 The Complex Plane -- 1.1 Complex Arithmetic -- 1.1.1 The Real Numbers -- 1.1.2 The Complex Numbers -- 1.1.3 Complex Conjugate -- 1.1.4 Modulus of a Complex Number -- 1.1.5 The Topology of the Complex Plane -- 1.1.6 The Complex Numbers as a Field -- 1.1.7 The Fundamental Theorem of Algebra -- 1.2 The Exponential and Applications -- 1.2.1 The Exponential Function -- 1.2.2 The Exponential Using Power Series -- 1.2.3 Laws of Exponentiation -- 1.2.4 Polar Form of a Complex Number 1.2.5 Roots of Complex Numbers1.2.6 The Argument of a Complex Number -- 1.2.7 Fundamental Inequalities -- 1.3 Holomorphic Functions -- 1.3.1 Continuously Differentiable and Ck Functions -- 1.3.2 The Cauchy-Riemann Equations -- 1.3.3 Derivatives -- 1.3.4 Definition of Holomorphic Function -- 1.3.5 The Complex Derivative -- 1.3.6 Alternative Terminology for Holomorphic Functions -- 1.4 Holomorphic and Harmonic Functions -- 1.4.1 Harmonic Functions -- 1.4.2 How They are Related -- 2 Complex Line Integrals -- 2.1 Real and Complex Line Integrals -- 2.1.1 Curves 2.1.2 Closed Curves2.1.3 Differentiable and C^k Curves -- 2.1.4 Integrals on Curves -- 2.1.5 The Fundamental Theorem of Calculus along Curves -- 2.1.6 The Complex Line Integral -- 2.1.7 Properties of Integrals -- 2.2 Complex Differentiabilityand Conformality -- 2.2.1 Limits -- 2.2.2 Holomorphicity and the Complex Derivative -- 2.2.3 Conformality -- 2.3 The Cauchy Integral Formula and Theorem -- 2.3.1 The Cauchy Integral Theorem, Basic Form -- 2.3.2 The Cauchy Integral Formula -- 2.3.3 More General Forms of the Cauchy Theorems -- 2.3.4 Deformability of Curves 2.4 A Coda on the Limitations of The Cauchy Integral Formula3 Applications of the Cauchy Theory -- 3.1 The Derivatives of a Holomorphic Function -- 3.1.1 A Formula for the Derivative -- 3.1.2 The Cauchy Estimates -- 3.1.3 Entire Functions and Liouville�s Theorem -- 3.1.4 The Fundamental Theorem of Algebra -- 3.1.5 Sequences of Holomorphic Functions and their Derivatives -- 3.1.6 The Power Series Representation of a Holomorphic Function -- 3.2 The Zeros of a Holomorphic Function -- 3.2.1 The Zero Set of a Holomorphic Function 3.2.2 Discreteness of the Zeros of a Holomorphic Function3.2.3 Discrete Sets and Zero Sets -- 3.2.4 Uniqueness of Analytic Continuation -- 4 Isolated Singularities and Laurent Series -- 4.1 The Behavior of a Holomorphic Function near an Isolated Singularity -- 4.1.1 Isolated Singularities -- 4.1.2 A Holomorphic Function on a Punctured Domain -- 4.1.3 Classification of Singularities -- 4.1.4 Removable Singularities, Poles, and Essential Singularities -- 4.1.5 The Riemann Removable Singularities Theorem -- 4.1.6 The Casorati-Weierstrass Theorem Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Fonctions d'une variable complexe. MATHEMATICS Complex Analysis. bisacsh Functions of complex variables fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052356 |
| title | A Guide to Complex Variables / |
| title_auth | A Guide to Complex Variables / |
| title_exact_search | A Guide to Complex Variables / |
| title_full | A Guide to Complex Variables / Steven G. Krantz. |
| title_fullStr | A Guide to Complex Variables / Steven G. Krantz. |
| title_full_unstemmed | A Guide to Complex Variables / Steven G. Krantz. |
| title_short | A Guide to Complex Variables / |
| title_sort | guide to complex variables |
| topic | Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Fonctions d'une variable complexe. MATHEMATICS Complex Analysis. bisacsh Functions of complex variables fast |
| topic_facet | Functions of complex variables. Fonctions d'une variable complexe. MATHEMATICS Complex Analysis. Functions of complex variables |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450270 |
| work_keys_str_mv | AT krantzsteveng aguidetocomplexvariables AT krantzsteveng guidetocomplexvariables |