# Lecture Notes

These are a selection of my notes of courses taught at KULAK or KULeuven. Most of these notes will only be useful to other KULeuven students, but not all of them: some notes I shared simply because they contain beautiful figures, like the report on Newton fractals, and some because they discuss interesting problems that I haven't found a detailed explanation on online, for example Takehome II of Relativity. If you're interested in the LATEX code, feel free to contact me.

B1 • 16-17 • nl • G0N30BN • 9 ECTS

### Analysis I

B2 • 17-18 • nl • G0N86BN • 6 ECTS

### Analysis II

B2 • 17-18 • nl • X0A43AN • 5 ECTS

### Numerical analysis

B2 • 17-18 • nl • X0C11AN • 9 ECTS

### Differential equations

B2 • 17-18 • nl • X0A65CN • 6 ECTS

### Algebra I

B3 • 18-19 • en • X0D95AE • 6 ECTS

### Topology

B3 • 18-19 • en • X0C93BN • 6 ECTS

### Complex analysis

B3 • 18-19 • nl • X0D42AN • 6 ECTS

### Bachelor Thesis

M1 • 19-20 • en • G0A84AE • 6 ECTS

### Algebraic Topology

M1 • 19-20 • en • G0B08AE • 6 ECTS

### Differential geometry

- Lecture notesDifferentiable manifolds, tangent vectors, vector fields, bundles, differential forms and integration, exterior derivative and Stokes theorem, de Rham cohomology, foliations, Lie groups and Lie algebras
- Takehome IEmbedding of product of spheres, derivative of a map, Lie bracket, flow, existence of Riemmanian metrics
- Takehome IIVolume form om spheres, orientability of RP², de Rham cohomology, folliations, Lie algebras and morphisms

M1 • 19-20 • en • G0B03AE • 6 ECTS

### Functional Analysis

- Lecture notesBanach, Hilbert spaces, bounded and compact compact operators, Hahn-Banach extension theorem, Baire category, open mapping, closed graph, uniform boundedness, weak topologies, Banach-Alaoglu, Hahn-Banach separation theorem, amenability of groups, Krein-Milman
- Takehome IPolar decomposition, Volterra operator, Borel functional calculus
- Takehome IIProperties of bounded operators, weak topology, ... Extreme points

M1 • 19-20 • en • G0I36AE • 6 ECTS

### Relativity

- Takehome IRiemann tensor of the 3-sphere, GPS time dilation due to gravity
- Takehome I: Mathematica notebookNotebook accompanying the first takehome
- Takehome IISolving Einsteins equation in vacuuum with Λ ≠ 0, potential of radial geodesics, Komar integral for angular momentum of Kerr metric
- Takehome II: Mathematica notebookNotebook accompanying the second takehome