Course information

Course Objectives
1. Understand Complex Numbers: Develop a solid foundation in complex numbers,
including geometric interpretation, square roots, and rational powers.
2. Explore Complex Functions: Learn the topology of the complex plane, one-to-one and
onto functions, limits, and continuity.
3. Analyze Differentiability: Study differentiability, Cauchy-Riemann equations, harmonic
functions, and power series.
4. Investigate Complex Integrals: Examine complex line integrals, the Cauchy-Goursat
theorem, and the winding number.
5. Apply Integral Theorems: Apply Cauchy’s integral formula, Morera’s theorem, and
compute line integrals.
Course Outcomes
1. Demonstrate proficiency in complex number operations, geometric interpretations, rational
powers and stereographic projection.
2. Apply topological concepts of the complex plane to understand the continuity and
differentiability of complex functions.
3. Solve problems involving differentiability, Cauchy-Riemann equations, and harmonic
functions.
4. Evaluate complex line integrals using the Cauchy-Goursat theorem and understand the
concept of winding number.
5. Compute integrals using Cauchy’s integral formula, understand Morera’s theorem, and
develop Taylor and Laurent series.