An introduction to complex analysis
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples...
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer US
2011.
Cham : Springer Nature |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to complex analysis, Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas, 2011, New York, Springer, 1 vol. (XIV-331 p.), 978-1-461-40194-0 • An Introduction to Complex Analysis, Texte imprimé, 9781461401964 • An Introduction to Complex Analysis, Texte imprimé, 9781489997166 |
Table des matières:
- Preface.-Complex Numbers.-Complex Numbers II
- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I
- Elementary Functions II
- Mappings by Functions
- Mappings by Functions II
- Curves, Contours, and Simply Connected Domains
- Complex Integration
- Independence of Path
- Cauchy Goursat Theorem
- Deformation Theorem
- Cauchy s Integral Formula
- Cauchy s Integral Formula for Derivatives
- Fundamental Theorem of Algebra
- Maximum Modulus Principle
- Sequences and Series of Numbers
- Sequences and Series of Functions
- Power Series
- Taylor s Series
- Laurent s Series
- Zeros of Analytic Functions
- Analytic Continuation
- Symmetry and Reflection
- Singularities and Poles I
- Singularities and Poles II
- Cauchy s Residue Theorem
- Evaluation of Real Integrals by Contour Integration I
- Evaluation of Real Integrals by Contour Integration II
- Indented Contour Integrals
- Contour Integrals Involving Multi valued Functions
- Summation of Series. Argument Principle and Rouch e and Hurwitz Theorems
- Behavior of Analytic Mappings
- Conformal Mappings
- Harmonic Functions
- The Schwarz Christoffel Transformation
- Infinite Products
- Weierstrass s Factorization Theorem
- Mittag Leffler s Theorem
- Periodic Functions
- The Riemann Zeta Function
- Bieberbach s Conjecture
- The Riemann Surface
- Julia and Mandelbrot Sets
- History of Complex Numbers
- References for Further Reading
- Index.