Final syllabus
- Chapters 1, 2
- Chapter 3: Sections 1–5. We also sketched Section 7.
- Chapter 4: Sections 1–10. You can find my lecture notes on Sections 8–10 here.
- Chapter 5: Sections 1–5. We skipped the section Abstract Fourier analysis in Section 5.3; I would recommend reading it, but it's not required. For background material, see my notes on the \(\ell^p\) spaces.
- Chapter 6: Sections 1–3, 6–8, and Section 1 in my note on multiindices. I taught Section 6.1 using little-o notation; see my note. I taught Section 6.6 less generally than the book does.
- Chapter 10: Sections 1–4. (I will not consider \(L^2\) convergence as part of the syllabus, only what I have taught in the videos.)
- For Norwegian speaking students: This list of Norwegian translations of mathematical terms.
Additional material
- In Chapters 4, 6 we will also use this set of notes on multiindices (updated 28.02.2020).
- In Chapter 6 we will use this set of notes on little-o and big-O notation.
- I have written a set of notes on the \(\ell^p\) spaces. We have gone through most of this in the lecture as examples, so this note is only meant as supporting material.
Background material
Many of the concepts in this course draw from finite-dimensional linear algebra (i.e., MAT1120). David Lay's Linear Algebra and Its Applications can be consulted if you need to revise this material. A more rigorous alternative to Lay is Friedberg, Insel, Spence: Linear Algebra.