# Learning material

All Jupyter notebooks can be beautified using the css file tma4125.css used found here.

#### Week 2 - Introduction and Preliminaries

• Lecture notes Introduction.pdf and corresponding Jupyter notebook Introduction.ipynb
• Regarding vector spaces, inner products, orthogonal projections etc. it might be a good idea to review the corresponding lecture notes 9-projeksjon.pdf from last autumn's Calculus 3 course.

#### Week 6 - 8 - Fourier series

• Lecture notes on Fourier series by Marten Nome (in Norwegian) fourierrekker.pdf
• To motivate the importance of understanding periodic functions, we watched a video on atrial fibrillation made by NHI (Norsk Helseinformatikk) in the beginning of lecture 10.
• My handwritten lecture notes on Fourier series containing both my English prepared ahead of the lecture and the Norwegian version written during the lecture. fourierseries_hwn.pdf . Note that this one lacks the long motivational discussion we had in lecture 10 (but I refer you to the video recording). The handwritten notes will be constantly updated while we progress with the topic.
• Jupyter notebook fourier_series_supplemental_material.ipynb provides supplemental material, in particular plots of some (partial sums of) Fourier series. You can also simply pull the notebook into your JupyterHub instance by clicking this link.
• Finally, here is a short video by Steve Brunton explaining/illustrating the Gibb's phenomena very nicely! Extremely nice setup for digital teaching and I can only encourage you to poke around in Steve Brunton's well-known and famous YouTube channel covering a lot of computational engineering/mathematics topics!

#### Week 8 Fourier transform

• My handwritten lecture notes on the Fourier transform containing both my English prepared ahead of the lecture and the Norwegian version written during the lecture fouriertransform_hwn.pdf.

#### Week 14 Wave Equation

• My handwritten lecture notes on the wave equation: English prepared ahead of the lecture WaveEquation.pdf and the Norwegian version written during the lecture WaveEquationLiveNotes.pdf (18th of April, 14:00). In the lecture we didn't discuss d'Alembert presentation for the wave equation on the real line, so please study the 2 last pages in the English version or in Marten's notes (see below).
• Lecture notes on wave equation by Marten Nome (in Norwegian bolgelikningen.pdf

### Supplemental material

I heavily use and reuse Morten Nome's excellent lecture notes from 2019 edition of TMA4215, in particular for Part I of the course. For the second part, the material will be mostly based on Anne Kvœrnø's Jupyter Notebooks.