SUBJECT

Title

Reading course in analysis

Type of instruction

lecture + practical

Level

master

Part of degree program
Credits

5

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Real functions. Functions of bounded variation. Riemann-Stieltjes integral, line integrals. The inverse and implicit function theorems. Optimum problems with constraints. Measure theory. The Lebesgue integral. Function spaces. Complex analysis. Cauchy's theorem and integral formula. Power series expansion of analytic functions. Isolated singular points, the residue theorem. Ordinary differential equations. Theorems on existence and uniqueness. Elementary methods.  Linear equations and systems. Hilbert spaces, orthonormal systems. Metric spaces, basic topological concepts, sequences, limits and continuity of functions. Numerical methods.

Readings
  • W. Rudin: Principles of mathematical analyis,
  • W. Rudin: Real and complex analyis,
  • F. Riesz and B. Szokefalvi-Nagy: Functional analysis.
  • G. Birkhoff and G-C. Rota: Ordinary Differential Equations,
  • J. Munkres: Topology.