All Jupyter notebooks can be beautified using the css file tma4125.css used found here.
Week 2 - Introduction and Preliminaries
- 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 2 and 3 - Polynomial interpolation
- The python code used in the Jupyter notebooks above is can be also found in polynomialinterpolation.py
Week 4 - Numerical integration
Week 5 - Numerical methods for nonlinear equations
- Hand-written lecture notes for Fixed-point iteration (pre-written, including extra material) fixed_point_iteration.pdf.
- Copy of the notes from the Fixed-point lecture (written during the lecture) fixed_point_lecture.pdf
- Hand-written lecture notes for Fixed-point iteration (pre-written, including extra material) newton_method.pdf
- Copy of the notes from the Newton lecture (written during the lecture) newton_lecture.pdf
- Notebook used during plenary seminar nonlinearequations.ipynb
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.
- 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 9-10 Laplace transform
- My handwritten lecture notes on the Laplace transform laplace_transform_hwn.pdf (10th of March, 21:37).
- The motivation for definition of the Laplace transform was inspired by Steve Brunton's short video lecture on the Laplace transform, so make sure to look the video as it also derives a formula for the inverse Laplace transform!
- Her is a short reminder on (a simplified version of) partial fraction decomposition (delbrøksoppspaltning), including an example.
- Lecture notes on Laplace transform by Marten Nome (in Norwegian) 01-laplacetransform.pdf
Week 11-12 Numerical methods for ordinary differential equations
Week 13-14 Heat Equation
- Lecture notes on heat equation by Marten Nome (in Norwegian varmelikningen.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
Week 15 Numerical methods for partial differential equations
- Lecture notes numerical methods for partial differential equations by Morten Nome (in Norwegian) 11-numerikk-for-pde.pdf
Week 16 Revision
- Handwritten lecture notes: Revisjonsforelesning.pdf