Matematika 4 is a required course for second-year undergraduates in the FMF physics program. These notes are from the winter semester of the 2019-20 academic year, when the course was taught by professor Bojan Magajna (lecture) and asst. professor Janez Šter (exercises). Material covered in the course includes:
- complex analysis: differentiability, the Cauchy-Riemman equations, integration, Cauchy’s theorem, Laurent series, singularities, the residue theorem, and the open mapping theorem and maximum modulus principle
- harmonic functions in two and three dimensions
- Fourier analysis: convolution, the Fourier transform in 1, 3, and n dimensions.
- partial differential equations: the heat equation and the wave equation
- an introduction to Sturm-Liouville theory
- power series methods for second-order linear differential equations