Videos from 2021

How to work through this material

Each video corresponds (roughly) to a section in?Spaces.?You should:

  • Watch the video (or just skim it, if you think you already know it)
  • Read (or skim) the corresponding section in?Spaces
  • Do as many of the accompanying exercises as you can.

If you're stuck, don't worry. Rewatch the video, reread the section in?Spaces,?reread earlier sections, discuss with a fellow student, ask your group teacher, or simply skip the exercise.

When you are certain that you have completed an exercise (or you have given up completely), you can check the solution?(not all exercises have worked solutions, unfortunately).

The more exercises you do, the better! If you should run out of exercises, don't be afraid of doing exercises that aren't listed here.

Videos

SectionVideoPDF
25–29 January
3.1Metric spacesPDF
3.2ConvergencePDF
3.2ContinuityPDF
3.3Open and closed setsPDF
1–5 February
3.3Alternative definitions of continuityPDF
3.4CompletenessPDF
3.4Banach's fixed point theoremPDF
3.5CompactnessPDF
8–12 February
3.5Compactness IIPDF
?Compactness IIIPDF
3.6Compactness IVPDF
3.7Completion of metric spaces?(this one is optional!)PDF
15–19 February
4.1Modes of continuityPDF
4.2Modes of convergencePDF
22–26 February
4.3Integrating sequences of functionsPDF
?Differentiating sequences of functionsPDF
2.2Lim inf and lim supPDF
4.4Power seriesPDF
1–5 March
4.5The space of bounded functionsPDF
4.6The space of bounded, continuous functionsPDF
4.7Ordinary differential equations IPDF
?Ordinary differential equations IIPDF
?Ordinary differential equations IIIPDF
(Note on multiindices)Multiindices IPDF
(Note on multiindices)Multiindices IIPDF
8–12 March
4.8The Arzela–Ascoli theoremPDF
4.9Convergence of numerical approximations of ODEsPDF
15–19 March
4.10The Weierstrass approximation theorem IPDF
?The Weierstrass approximation theorem IIPDF
5.1Normed vector spaces I – preliminariesPDF
?Normed vector spaces II – equivalent normsPDF
5.2Series and basesPDF
5–9 April
5.3Inner product spacesPDF
5.4Linear operators IPDF
?Linear operators II – boundednessPDF
?Linear operators III – the space?\(\mathcal{L}(V,W)\).PDF
5.5Invertible linear operators IPDF
?Invertible linear operators II – Neumann seriesPDF
12–16 April
10.1Fourier series – Introduction and motivationPDF
10.2Fourier convergence IPDF
?Fourier convergence IIPDF
19–23 April
10.3The Dirichlet kernelPDF
10.4Cesàro convergence of Fourier seriesPDF
26–30 April
6.1What is a derivative?PDF
?The Fréchet derivative I – DefinitionPDF
?The Fréchet derivative II – CalculusPDF
6.2The Gateaux derivativePDF
6.3The mean value theoremPDF
3–7 May
6.7The inverse function theoremPDF
6.6Partial derivativesPDF
6.8The implicit function theorem IPDF
6.8The implicit function theorem IIPDF

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Publisert 22. jan. 2021 11:43 - Sist endret 15. jan. 2026 09:32