Syllabus
Metric spaces: completeness, connectivity, compactness.
Series: series of real/complex numbers, power series and series of functions. Different types of convergence, operations with series. Fourier series.
Complex analysis: holomorphic functions, Cauchy formula - poles of a function, applications.
Introduction to differential equations: equations with separated variables, linear equations. Existence of a solution, numerical view.
Annotation
The third part of the mathematical analysis course for students of computer science. It explains more advanced areas with an emphasis on parts useful for computer science.
It will be assumed that the students understand material covered by Mathematical Analysis 1 and 2.