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Introduction to complex analysis / / H.A. Priestley
| Introduction to complex analysis / / H.A. Priestley |
| Autore | Priestley H. A (Hilary A.) |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Oxford : , : Oxford University Press, , 2023 |
| Descrizione fisica | 1 online resource (343 p.) |
| Disciplina | 515.9 |
| Collana | Oxford scholarship online |
| Soggetto topico |
Mathematical analysis
Functions of complex variables |
| ISBN |
1-383-02422-7
0-19-103720-6 0-19-158333-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; Notation and terminology; 1. The complex plane; Complex numbers; Algebra in the complex plane; Conjugation, modulus, and inequalities; Exercises; 2. Geometry in the complex plane; Lines and circles; The extended complex plane and the Riemann sphere; Möbius transformations; Exercises; 3. Topology and analysis in the complex plane; Open sets and closed sets in the complex plane; Convexity and connectedness; Limits and continuity; Exercises; 4. Paths; Introducing curves and paths; Properties of paths and contours; Exercises; 5. Holomorphic functions
Differentiation and the Cauchy-Riemann equationsHolomorphic functions; Exercises; 6. Complex series and power series; Complex series; Power series; A proof of the Differentiation theorem for power series; Exercises; 7. A cornucopia of holomorphic functions; The exponential function; Complex trigonometric and hyperbolic functions; Zeros and periodicity; Argument, logarithms, and powers; Holomorphic branches of some simple multifunctions; Exercises; 8. Conformal mapping; Conformal mapping; Some standard conformal mappings; Mappings of regions by standard mappings; Building conformal mappings Exercises9. Multifunctions; Branch points and multibranches; Cuts and holomorphic branches; Exercises; 10. Integration in the complex plane; Integration along paths; The Fundamental theorem of calculus; Exercises; 11. Cauchy's theorem: basic track; Cauchy's theorem; Deformation; Logarithms again; Exercises; 12. Cauchy's theorem: advanced track; Deformation and homotopy; Holomorphic functions in simply connected regions; Argument and index; Cauchy's theorem revisited; Exercises; 13. Cauchy's formulae; Cauchy's integral formula; Higher-order derivatives; Exercises 14. Power series representationIntegration of series in general and power series in particular; Taylor's theorem; Multiplication of power series; A primer on uniform convergence; Exercises; 15. Zeros of holomorphic functions; Characterizing zeros; The Identity theorem and the Uniqueness theorem; Counting zeros; Exercises; 16. Holomorphic functions: further theory; The Maximum modulus theorem; Holomorphic mappings; Exercises; 17. Singularities; Laurent's theorem; Singularities; Meromorphic functions; Exercises; 18. Cauchy's residue theorem; Residues and Cauchy's residue theorem Calculation of residuesExercises; 19. A technical toolkit for contour integration; Evaluating real integrals by contour integration; Inequalities and limits; Estimation techniques; Improper and principal-value integrals; Exercises; 20. Applications of contour integration; Integrals of rational functions; Integrals of other functions with a finite number of poles; Integrals involving functions with infinitely many poles; Integrals involving multifunctions; Evaluation of definite integrals: overview (basic track); Summation of series; Further techniques; Exercises; 21. The Laplace transform Basic properties and evaluation of Laplace transforms |
| Record Nr. | UNINA-9910971001503321 |
Priestley H. A (Hilary A.)
|
||
| Oxford : , : Oxford University Press, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to complex analysis / / H. A. Priestley
| Introduction to complex analysis / / H. A. Priestley |
| Autore | Priestley H. A (Hilary A.) |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Oxford, England : , : Oxford University Press, , 2005 |
| Descrizione fisica | 1 online resource (343 p.) |
| Disciplina | 515.9 |
| Soggetto topico |
Mathematical analysis
Functions of complex variables |
| ISBN |
1-383-02422-7
0-19-103720-6 0-19-158333-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; Notation and terminology; 1. The complex plane; Complex numbers; Algebra in the complex plane; Conjugation, modulus, and inequalities; Exercises; 2. Geometry in the complex plane; Lines and circles; The extended complex plane and the Riemann sphere; Möbius transformations; Exercises; 3. Topology and analysis in the complex plane; Open sets and closed sets in the complex plane; Convexity and connectedness; Limits and continuity; Exercises; 4. Paths; Introducing curves and paths; Properties of paths and contours; Exercises; 5. Holomorphic functions
Differentiation and the Cauchy-Riemann equationsHolomorphic functions; Exercises; 6. Complex series and power series; Complex series; Power series; A proof of the Differentiation theorem for power series; Exercises; 7. A cornucopia of holomorphic functions; The exponential function; Complex trigonometric and hyperbolic functions; Zeros and periodicity; Argument, logarithms, and powers; Holomorphic branches of some simple multifunctions; Exercises; 8. Conformal mapping; Conformal mapping; Some standard conformal mappings; Mappings of regions by standard mappings; Building conformal mappings Exercises9. Multifunctions; Branch points and multibranches; Cuts and holomorphic branches; Exercises; 10. Integration in the complex plane; Integration along paths; The Fundamental theorem of calculus; Exercises; 11. Cauchy's theorem: basic track; Cauchy's theorem; Deformation; Logarithms again; Exercises; 12. Cauchy's theorem: advanced track; Deformation and homotopy; Holomorphic functions in simply connected regions; Argument and index; Cauchy's theorem revisited; Exercises; 13. Cauchy's formulae; Cauchy's integral formula; Higher-order derivatives; Exercises 14. Power series representationIntegration of series in general and power series in particular; Taylor's theorem; Multiplication of power series; A primer on uniform convergence; Exercises; 15. Zeros of holomorphic functions; Characterizing zeros; The Identity theorem and the Uniqueness theorem; Counting zeros; Exercises; 16. Holomorphic functions: further theory; The Maximum modulus theorem; Holomorphic mappings; Exercises; 17. Singularities; Laurent's theorem; Singularities; Meromorphic functions; Exercises; 18. Cauchy's residue theorem; Residues and Cauchy's residue theorem Calculation of residuesExercises; 19. A technical toolkit for contour integration; Evaluating real integrals by contour integration; Inequalities and limits; Estimation techniques; Improper and principal-value integrals; Exercises; 20. Applications of contour integration; Integrals of rational functions; Integrals of other functions with a finite number of poles; Integrals involving functions with infinitely many poles; Integrals involving multifunctions; Evaluation of definite integrals: overview (basic track); Summation of series; Further techniques; Exercises; 21. The Laplace transform Basic properties and evaluation of Laplace transforms |
| Record Nr. | UNINA-9910787994303321 |
|
Priestley H. A (Hilary A.)
|
||
| Oxford, England : , : Oxford University Press, , 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||