- Continuous Vector-Valued Functions
- Some Linear Algebra
- Differentiable Functions
- Uniform convergence and applications
- Convergence of sequences and series of functions
- Introduction to complex valued functions
Objectives: By the end of the module the students should be able to:
- Understand uniform and pointwise convergence of functions together with properties of the limit function
- Study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions
- Study complex differentiability (Cauchy-Riemann equations) and complex power series
- Study contour integrals: Cauchy's integral formulas and applications.
Books: There is no recommended textbook for the course. A complete set of lecture notes will be provided.