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Complex Analysis : A Modern First Course in Function Theory
| Complex Analysis : A Modern First Course in Function Theory |
| Autore | Muir Jerry R |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New York : , : John Wiley & Sons, Incorporated, , 2015 |
| Descrizione fisica | 1 online resource (277 pages) |
| Disciplina | 515 |
| Altri autori (Persone) | MuirJerry R., Jr |
| Soggetto topico |
Geometric function theory
Geometry Numbers, Complex |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9781118705278
9781118705223 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910795816003321 |
Muir Jerry R
|
||
| New York : , : John Wiley & Sons, Incorporated, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex Analysis : A Modern First Course in Function Theory
| Complex Analysis : A Modern First Course in Function Theory |
| Autore | Muir Jerry R |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New York : , : John Wiley & Sons, Incorporated, , 2015 |
| Descrizione fisica | 1 online resource (277 pages) |
| Disciplina | 515 |
| Altri autori (Persone) | MuirJerry R., Jr |
| Soggetto topico |
Geometric function theory
Geometry Numbers, Complex |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9781118705278
9781118705223 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910820273803321 |
|
Muir Jerry R
|
||
| New York : , : John Wiley & Sons, Incorporated, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||