Wes - Introduction to Complex Analysis
- Offered byCoursera
Introduction to Complex Analysis at Coursera Overview
Duration | 27 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
Introduction to Complex Analysis at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Intermediate Level
- Approx. 27 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
Introduction to Complex Analysis at Coursera Course details
- This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today. Each module consists of five video lectures with embedded quizzes, followed by an electronically graded homework assignment. Additionally, modules 1, 3, and 5 also contain a peer assessment.
- The homework assignments will require time to think through and practice the concepts discussed in the lectures. In fact, a significant amount of your learning will happen while completing the homework assignments. These assignments are not meant to be completed quickly; rather you'll need paper and pen with you to work through the questions. In total, we expect that the course will take 6-12 hours of work per module, depending on your background.
Introduction to Complex Analysis at Coursera Curriculum
Introduction to Complex Numbers
History of Complex Numbers
Algebra and Geometry in the Complex Plane
Polar Representation of Complex Numbers
Roots of Complex Numbers
Topology in the Plane
Lecture Slides
Lecture Slides
Lecture Slides
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Lecture Slides
Module 1 Homework
Complex Functions and Iteration
Complex Functions
Sequences and Limits of Complex Numbers
Iteration of Quadratic Polynomials, Julia Sets
How to Find Julia Sets
The Mandelbrot Set
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Module 2 Homework
Analytic Functions
The Complex Derivative
The Cauchy-Riemann Equations
The Complex Exponential Function
Complex Trigonometric Functions
First Properties of Analytic Functions
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Module 3 Homework
Conformal Mappings
Inverse Functions of Analytic Functions
Conformal Mappings
Mobius transformations, Part 1
Mobius Transformations, Part 2
The Riemann Mapping Theorem
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Module 4 Homework
Complex Integration
Complex Integration
Complex Integration - Examples and First Facts
The Fundamental Theorem of Calculus for Analytic Functions
Cauchy?s Theorem and Integral Formula
Consequences of Cauchy?s Theorem and Integral Formula
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Module 5 Homework
Power Series
Infinite Series of Complex Numbers
Power Series
The Radius of Convergence of a Power Series
The Riemann Zeta Function And The Riemann Hypothesis
The Prime Number Theorem
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Lecture Slides
Module 6 Homework
Laurent Series and the Residue Theorem
Laurent Series
Isolated Singularities of Analytic Functions
The Residue Theorem
Finding Residues
Evaluating Integrals via the Residue Theorem
Bonus: Evaluating an Improper Integral via the Residue Theorem
Lecture Slides
Lecture Slides
Lecture Slides
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Lecture Slides
Module 7 Homework
Final Exam
Final Exam
Introduction to Complex Analysis at Coursera Admission Process
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