MAT3102: Complex Variables

Complex variables, is the branch of Mathematics that investigates functions of complex numbers, i.e., functions whose independent and dependent variables are both complex numbers. The course extends concepts from the analysis of real valued functions to complex functions. This course is of enormous practical use in applied Mathematics and Physics. It covers topics which include: Complex numbers and functions; Analytic and Harmonic functions; The basic Transcendental Functions; and Contour Integration.

Course Objectives
On successful completion of this course unit, the learners should be able: 

• Extend concepts of analysis of real variables to complex numbers like sequences and series 
• Differentiate and integrate complex functions 
• Carry out contour integration 
• Perform standard algebraic operations on complex numbers 
• Represent complex numbers on Argand diagram 
• Work with functions of a complex variable 
• Extend convergence and continuity of results to complex plane viii. State, prove and apply Cauchy-Riemann equations 
• State, prove and apply Cauchy-Integral formula 
• Find Analytic functions 
• State, prove and apply Cauchy Residue Theorem. 

Expected Learning Outcome
This course unit is meant: 

• To discuss the basic competence in the concepts, principle, procedures and application of differentiable complex-valued functions of a single complex variable.  
• To encourage orderliness, speed and accuracy in the presentation of mathematics. 
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly. 
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills. 
• To build a strong foundation in Complex Variables as preparation for subsequent courses in mathematics and other sciences.