Mathematics 4

• Lecture notes
• Oral exam notes

Course description

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