Some Info on the Course Applied Analysis, Part 2
- The first section on the Fourier transform will be oriented on the Handouts 1 - 5 at this page.
- Here you can find another useful reference.
- 23-11-2016. After the first lecture I became aware of a few imprecise statements of the proof of the Fourier inversion formula in the Handouts which are linked above. Please find a more detailed (and correct)
version of the proof of the Fourier inversion formula here.
- 23-11-2016. Our results on approximate identities are not only useful for proving the Fourier inversion formula but they are crucial for a large class of approximation problems. As an exercise you can prove for yourself the famous Weierstrass approximation theorem using this blueprint.
- 28-11-2016. Check out the new version of my pdf writeup here! Everything `left as an exercise' can be presented on Thursday! As another exercise solve the linear wave equation using the Fourier transform and/or compute the (distributional) Fourier transform of the Heaviside function.
- 15-12-2016. New version of the script available here! There are lots of exercises!
- 11-01-2017. New version of the script available here! New exercises are available here.
- 27-01-2017. New version of the script available here!
- 02-02-2017. New (and, for the time being, FINAL) version of the script available here! Here are the MATLAB codes for a very simple filtered backprojection algorithm.