Learning material

• the lecture notes are available as the slides I used: 01-Preliminaries.pdf (V2, fixed typos) and a Jupyter notebook 01-Preliminaries.ipynb for some numerical examples.
• Regarding vector spaces, inner products, orthogonal projections etc. it might be a good idea to review the corresponding lecture notes, e.g. 9-projeksjon.pdf from autumn 2020s Calculus 3 course.

• the lecture notes for polynomial interpolation methods are available as slides 02-Polynomial-interpolation-methods.pdf (V2, fixed typos) and a Jupyter notebook 02-polynomial-interpolation-methods.ipynb (V2, corrected typos)
• the lecture notes for polynomial interpolation error analysis are available as slides 02-polynomial-interpolation-error-analysis.pdf and a Jupyter notebook 02-polynomial-interpolation-error-analysis.ipynb (V3, update docmentation). Note that the function chebyshev_nodes(a, b, n) returns n points in order to work the same as linespace(alb,n) (i.e. you can easily exchange both). For a polynomial of degree n you have to call chebyshev_nodes(a, b, n+1).

• lecture notes for numerical integration are available as 03-Numerical-integration.pdf (V2, 2002-04-25, corrected a typo in the degree of exactness for Simpson) and a Jupyter notebook 03-numerical-integration.ipynb
• Preliminaries: Some numerical integration methods were already considered in Calculus 1, Week 42, please review this material, e.g. by watching video recording of lecture 08 (in Norwegian).

• lecture notes for numerical solution of nonlinear equations are available as 04-Nonlinear-Equations.pdf and the corresponding Jupyter notebook 04-numerical-solution-of-nonlinear-equations.ipynb.

• lecture notes for Laplace transform, Part I 05a-Laplace-Transform-I.pdf (V2 - there was a typo in the Laplace transforms of $\cosh$ and $\sinh$)
• lecture notes for Laplace transform, Part II 05b-Laplace-Transform-II.pdf (for the second week) and a small notebook for plotting 05b-The-Laplace-Transform-VI.ipynb
• Here 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

• lecture notes for the numerical methods lectures, first week, is 06a-Numerical-solution-of-ODEs.pdf and the corresponding Jupyter notebook is 06a-Numerical-solution-of-ODEs.ipynb.
• lecture notes for the numerical methods lectures, second week (Part I), is 06b-Runge-Kutta-methods-and-adaptivity.pdf and the corresponding Jupyter notebook is 06b-Runge-Kutta-and-adaptivity.ipynb.
• lecture notes for the numerical methods lectures, second week (Part II), is 06c-Numerical-stability-in-ODEs.pdf and the corresponding Jupyter notebook is 06c-Numerical-stability-in-ODEs.ipynb.

• lecture notes for the first week are available as 07a-Fourier-Series-I.pdf (V2, note that there was a typo in both the $b_n$ on slide 26 – now correct with a $\sin$ and on slide 28 where it is times $\mathrm{I}$ and not a vision by it) and a small accompanying Jupyter notebook 07a-Fourier-Series-I.ipynb.
• lecture notes for the second week are available as 07b-Fourier-Series-II.pdf (V2, fixed typos, added a slide about convolution), the proof for Lipschitz continuous functions is given here
• you can also check the Lecture notes on Fourier series by Marten Nome (in Norwegian) fourierrekker.pdf
• for complex Fourier series a nice visualisation was made by 3blue1brown in his video about Fourier series

• lecture notes for the Fourier Transform are available as 08-Fourier-Transform.pdf as well as a small notebook on the DFT 08-Discrete-Fourier-Transform.ipynb
• 3blue1brown has a nice video on Fourier transform as well.

• lecture notes for the Heat Equation are available as 09-Heat-Equation.pdf (V3, fixed typos, added summary).
• Lecture notes on heat equation by Marten Nome (in Norwegian) varmelikningen.pdf

• lecture notes for the Wave Equation are available as 10-Wave-Equation.pdf
• Lecture notes on wave equation by Marten Nome (in Norwegian) bolgelikningen.pdf

• Lecture notes for Numerical Methods for PDEs are available as 11-numerical-methods-for-PDEs.pdf as well as a Jupyter notebook 11-numerical-methods-for-PDEs.ipynb
• Lecture notes numerical methods for partial differential equations by Morten Nome (in Norwegian) 11-numerikk-for-pde.pdf

For the Wednesday summary and question time I wrote a (very) short summary of the course 12-short-summary.pdf

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.