Content:

• 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.