About this Course
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
What You'll Learn
- Understand algebraic and geometric properties of complex numbers
- Apply differentiation and integration techniques in complex analysis
- Explore complex dynamics and power series representations
- Solve advanced problems using complex analysis concepts
Prerequisites
- Basic familiarity with complex analysis concepts and terminology
- Readiness to practice via exercises and case studies
Instructors
Dr. Petra Bonfert-Taylor
Former Professor of Mathematics at Wesleyan University / Professor of Engineering at Thayer School of Engineering at Dartmouth