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Source : www.coursera.org
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6 séquences
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Niveau : Introductif
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Calculs
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Langue : Anglais
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288 points
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Les infos clés
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Formation gratuite
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Certification gratuite
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36 heures de cours
En résumé
In this course we’ll explore complex analysis, complex dynamics, and some applications of these topics.
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Le programme
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.
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Les intervenants
- - Mathematics and Computer Science
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Le concepteur
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.
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La plateforme
Coursera est une entreprise numérique proposant des formations en ligne ouverte à tous fondée par les professeurs d'informatique Andrew Ng et Daphne Koller de l'université Stanford, située à Mountain View, Californie.
Ce qui la différencie le plus des autres plateformes MOOC, c'est qu'elle travaille qu'avec les meilleures universités et organisations mondiales et diffuse leurs contenus sur le web.
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