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Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi
| Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi |
| Autore | Shakarchi Rami |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 246 p. 17 illus.) |
| Disciplina | 515/.9 |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-1534-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy’s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy’s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy’s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy’s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen’s Formula -- XII.1 Jensen’s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and Meromorphic Functions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. |
| Record Nr. | UNINA-9910480773503321 |
Shakarchi Rami
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi
| Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi |
| Autore | Shakarchi Rami |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 246 p. 17 illus.) |
| Disciplina | 515/.9 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-1534-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy’s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy’s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy’s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy’s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen’s Formula -- XII.1 Jensen’s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and Meromorphic Functions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. |
| Record Nr. | UNINA-9910789219403321 |
|
Shakarchi Rami
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi
| Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi |
| Autore | Shakarchi Rami |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 246 p. 17 illus.) |
| Disciplina | 515/.9 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-1534-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy’s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy’s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy’s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy’s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen’s Formula -- XII.1 Jensen’s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and Meromorphic Functions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. |
| Record Nr. | UNINA-9910828903003321 |
|
Shakarchi Rami
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||