A Bootcamp to Complex Analysis

This course A Bootcamp to Complex Analysis provides an introduction to the theory of complex functions of a complex variable. It opens by introducing the complex plane, followed by the algebra and geometry of complex numbers. Like in Real Analysis, we will make our way through algebraic processing, topology, complex dynamics, Julia sets, the relationship of exponential function and the imaginary unit i, analytic function etc. In this course, we are going to learn different concepts than the ones we have already learned in school as Real Analysis.  In real numbers, we can approach infinity by either heading towards the right side or left side on the number scale while in the complex plane, we have infinite ways of approaching infinity. Likewise, with the aid of the Residue theorem, which is the pinnacle of this learning concept, with a technical advantage we shall be able to solve integrals that real analysis is not capable of. Complex analysis has real-life applications spread over all science subjects, all fields of engineering disciplines, and industrial applications too.

The course is divided into 5 sections that are spread over 40 video lectures with embedded quizzes for self-assessment and self-evaluation.

The optional homework/practice assignments are for advanced learners to take up their skills via stages: Remembering-Understanding-Application-Evaluation-Creation, the cognitive domain of Bloom’s Taxonomy. Infact, a significant amount of your learning will happen while completing the homework assignments that will need pen and paper. We anticipate basic knowledge of algebra, geometry, and calculus. However, amateurs can also take this as a primary course for building a level of creative application.

Course Outcomes

• Definition of CN,
• It’s algebraic processing,
• Topology,
• Complex Dynamics,
• Plotting of complex functions,
• Iteration – Julia Sets, Limit & Continuity,
• Exponential function and complex numbers – Euler’s Identity,
• Analytic Functions.