General

Course Information

Introduction

This is a third year second semester course and is offered to those who have done MMA 300 Real Analysis I. The course begins with a brief introduction to differential calculus of complex valued functions and is extended to integral calculus of the same functions via Cauchy integral theorem and formula together with Residue theorem. Finally the course entails Taylor and Laurent series for complex valued functions. 

The Course will be offered online and there will also be a mid-semester face-to-face meeting between the course instructor and the other course participants. The participants are required to be active most of the times and to engage the instructor whenever you do not understand a concept.

The main prerequisites for the course are MMA 100 Basic Mathematics, MMA 103: Linear Algebra, Introduction to Analysis and Real Analysis I, and Calculus I and II.

Course Requirement

This course will require at least 60 hours for effective coverage of the course content. That translate to at least 6 hours of your time per week. Besides, each topic has lecture notes together with the exercises for the participants which you are required to solve and submit every week. Late submission is not allowed. In addition to that you will be required to have the following:

• A laptop/desktop or smartphone together with internet connection.
• A scientific calculator and,
• A pen and a writing pad.

The course will be evaluated through continuous assessment tests and end semester examination.

• Mastery quizzes 15%
• Test quizzes 15%
• End of Semester exam 70%.

Pass mark for the course is 40% of the total score.

Once opened, Mastery quizzes will remain open for the duration of the course and can be attempted as many times as you wish. Test quizzes on the other hand will have limited availability.

There will be no extensions to deadlines. Plan your time well to meet  the set deadlines.

Course Objectives

By the end of this course you should be able to:

1. Define limits of complex valued functions and compute the limits of various functions at various points.
2. Explain the meaning of continuous functions at various points in the complex plain.
3. Define the derivative of a complex valued function and use these derivatives to determine whether a function is Harmonic or not.
4. State and prove Cauchy's integral theorem and apply it to compute the integral of various function within certain regions (contours).
5. Compute the Taylor and Laurent series of complex valued functions within some region.
6. Apply Residue theorem to integrate functions that can be expressed in Laurent series.