Course contents: Complex analysis: complex numbers, complex functions, analytic functions, sequences, series of complex functions, integration, calculus of integral balances. Fourier analysis: periodic functions, harmonic functions, trigonometric series, Fourier series, exponential form of Fourier series, derivative and integration of Fourier series. Taylor and McLaurin series, approximate calculations. Functions of several variables: vector analysis, curve theory, partial derivatives, Green’s, Stokes and divergence theorems, multiple integrals.

At the end of the course the student will be able to:

• Analyze and solve problems with complex numbers and complex functions
• Computes Taylor and McLaurin series
• Computes Fourier transforms as well as their inverses
• Analyze and solve problems with functions of many variables, and calculate partial derivatives
• Analyze and solve problems with vector functions
• Computes curvilinear, surface and spatial integrals

Assessment: 3 hours written exams. Mid-exams are possible with weight 40%.