- Sur www.coursera.org
Analysis of a Complex Kind
Cours
en
Anglais
36 h
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- À son rythme
- Accès libre
- Certificat gratuit
- 6 séquences
- Niveau Introductif
Détails du cours
Déroulé
Week One: Introduction to complex numbers, their geometry and algebra, working with complex numbers.
Week Two: The Mandelbrot set, Julia sets, a famous outstanding conjecture, history of complex numbers, sequences of complex numbers and convergence, complex functions.
Week Three: Complex differentiation and the Cauchy-Riemann equations.
Week Four: Conformal mappings, Möbius transformations and the Riemann mapping theorem.
Week Five: Complex integration, Cauchy-Goursat theorem, Cauchy integral formula, Liouville's Theorem, maximum principle, fundamental theorem of algebra.
Week Six: Power series representation of analytic functions, singularities, the Riemann zeta function, Riemann hypothesis, relation to prime numbers.
Week Two: The Mandelbrot set, Julia sets, a famous outstanding conjecture, history of complex numbers, sequences of complex numbers and convergence, complex functions.
Week Three: Complex differentiation and the Cauchy-Riemann equations.
Week Four: Conformal mappings, Möbius transformations and the Riemann mapping theorem.
Week Five: Complex integration, Cauchy-Goursat theorem, Cauchy integral formula, Liouville's Theorem, maximum principle, fundamental theorem of algebra.
Week Six: Power series representation of analytic functions, singularities, the Riemann zeta function, Riemann hypothesis, relation to prime numbers.
Prérequis
Aucun.
Intervenants
- - Mathematics and Computer Science
Éditeur
At Wesleyan, distinguished scholar-teachers work closely with students, taking advantage of fluidity among disciplines to explore the world with a variety of tools. The university seeks to build a diverse, energetic community of students, faculty, and staff who think critically and creatively and who value independence of mind and generosity of spirit.
Plateforme
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