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Viser: An Introduction to Complex Analysis
An Introduction to Complex Analysis Vital Source e-bog
Ravi P. Agarwal, Kanishka Perera og Sandra Pinelas
(2011)
An Introduction to Complex Analysis
Ravi P. Agarwal, Kanishka Perera og Sandra Pinelas
(2011)
Sprog: Engelsk
Detaljer om varen
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Springer Nature (Juli 2011)
- Forfattere: Ravi P. Agarwal, Kanishka Perera og Sandra Pinelas
- ISBN: 9781461401957
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Detaljer om varen
- 1. Udgave
- Hardback: 346 sider
- Udgiver: Springer (Juli 2011)
- Forfattere: Ravi P. Agarwal, Kanishka Perera og Sandra Pinelas
- ISBN: 9781461401940
I. - 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
I. - 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. - The 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 Theorem. -Periodic Functions. -The Riemann Zeta Function. -Bieberbach's Conjecture. -Riemann Surfaces. -Julia and Mandelbrot Sets. -History of Complex Numbers. -References for Further Reading. -Index