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Source: www.coursera.org
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6 sequences
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Level : Introductory
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Calculus
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Language : English
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288 points
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Key Information
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Free access
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Free certificate
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36 hours in total
About the content
In this course we’ll explore complex analysis, complex dynamics, and some applications of these topics.
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Syllabus
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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Instructors
- - Mathematics and Computer Science
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Content Designer
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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Platform
Coursera is a digital company offering massive open online course founded by computer teachers Andrew Ng and Daphne Koller Stanford University, located in Mountain View, California.
Coursera works with top universities and organizations to make some of their courses available online, and offers courses in many subjects, including: physics, engineering, humanities, medicine, biology, social sciences, mathematics, business, computer science, digital marketing, data science, and other subjects.
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