Introduction to Complex Analysis
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.
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Syllabus
Syllabus - What you will learn from this course
Week 1
Introduction to Complex Numbers
Week 2
Complex Functions and Iteration
Week 3
Analytic Functions
Week 4
Conformal Mappings
Week 5
Complex Integration
Week 6
Power Series
Week 7
Laurent Series and the Residue Theorem
Week 8
Final Exam
FAQ
When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.
Reviews
it was very challenging course , not so easy to pass the assignments but if you have gone through lectures, it will helps a lot while doing the assignments especially the final quiz
Excellent lectures. Great insights into how complex integration works. Tests and assignments are fair. Extra practice problems would be nice to help understanding.
Very thorough course. From basic to advanced concepts, Petra does an amazing job of conveying you through all the concepts in a perfectly clear and robust manner.
The prof makes it easy to understand yet fascinating. I enjoyed video checkpoints, quizzes and peer reviewed assignments. This course encourages you to think and discover new things.
