By the end of this course, a student will:
- Understand in details the complex number system and the complex plane.
- Use functions of a complex variable and explore their properties.
- Understand the concepts of the derivative of a complex function and analyticity of a function.
- Make calculations with elementary functions of a complex variable.
- Evaluate line integrals and prove results using the Cauchy theorem and the Cauchy integral formulas.
- Freely use of complex sequences and infinite series, Laurent series, residues and the residue theorem and apply them to various problems.
- Understand the concepts of conformal mappings, geometrical principles, compactness, and the Riemann mapping theorem.