Lecture plan

This section contains descriptions of the material covered in lectures, all of which are examinable unless explicitly exempted.

Part I: Laplace transforms and Fourier analysis.

This part introduces you to the Laplace transform (a smart way to transform differential equations into algebraic ones, that might be easier to solve). After Laplace transforms you will learn about Fourier series, which express simple functions as sums of sinus- and cosinus signals, and their extension, the Fourier transforms. These topics have applications in signal processing, image compression and many other areas in applied mathematics and the mathematical sciences. We will also discuss functions of several variables, and how to solve partial differential equations (PDEs), e.g., the heat equations, by Fourier series.

The material of this part of the lecture is based on Advanced Engineering Mathematics by Erwin Kreyszig, 10th edition, John Wiley & Sons, 2011, and the chapter numbers in the table below refer to this textbook. Note that this lecture plan is not set in stone and might be subject to (smaller) modifications.

The .ipynb files can be run by Jupyter Notebook. If Jupyter Notebook is not already installed, we recommend using the anaconda distribution, a detailed installation guide for which can be found here. The css file called at the beginning of the notebooks can be found here: Cascade Stylesheet file for Jupyter notebooks.

Week Chapter Content Lecture Notes Jupyter notebooks
Markus Grasmair Helge Holden & Elisabeth Köbis
34 6.1, 6.2 Laplace transforms, transform of derivatives, ODE Lecture 1, August 18
Forelesning 2, 21. august Slides - 21. august
lecture1.pdf lecture1_withnotes.pdf
lecture2.pdf lecture2withnotes.pdf (last line on page 10 is corrected in this version)
35 6.3 - 6.5 Heaviside function, delta function, convolution Forelesning 3, 25. august Slides - 25. august
Forelesning 4, 28. august Slides - 28. august Konvolusjon
lecture3.pdf lecture2withnotesupdated24-08-20.pdf lecture3withnotes.pdf lecture3withnotesupdated.pdf
lecture4.pdf lecture4withnotes.pdf
36 6.6, 6.7, 11.1 systems of ODEs; Fourier series Forelesning 5, 1. september Slides - 1. september
Forelesning 6, 4. september Slides - 4. september
lecture5withnotes.pdf
lecture6withnotes.pdf
Plot of Fourier series
37 11.2 - 11.4 Fourier series: representations and convergence Forelesning 7, 8. september Slides - 8. september
Forelesning 8, 11. september Slides - 11. september
lecture7withnotes.pdf
lecture8withnotes.pdf
Half-range expansions
Forced oscillations
38 11.7, 11.9 Fourier integral and transform Forelesning 9, 15. september Slides - 15. september
Forelesning 10, 18. september Slides - 18. september
lecture9.pdflecture9withnotes.pdffouriertransform.pdf
lecture10.pdflecture10withnotes.pdf
DFT
39 12.1 - 12.4 Wave equation Forelesning 11, 22. september Slides - 22. september
Forelesning 12, 25. september Slides - 25. september
lecture_11.pdf lecture12.pdf some
Solutions of 1d wave equation
40 12.5 - 12.7 Heat equation Forelesning 13, 29. september Slides - 29. september
Forelesning 14, 2. oktober Slides - 2. oktober
lecture13.pdf lecture14.pdf Solution of heat equation


Part II: Numerical methods. The curriculum is covered by the notes found in Jupyter notes, which will be made available below. For now, you can have a look at the notes from 2018. There are also pdf-versions of the notes available. The .ipynb files can be run by Jupyter Notebook. If Jupyter Notebook is not already installed, we recommend using the anaconda distribution, a detailed installation guide for which can be found here.

Alternatively, you can also use the Jupyter hub. There you can upload the .ipynb files and run them on a dedicated server. In order to be able to use the Jupyter hub, you have to be logged on to your Feide account.

Instructions for how to log in can also be found on the course-related blackboard page.

About programming: You are supposed to be able to read and understand simple python code, and to do small modifications on a given code. Possible small syntax errors will have no influence on the grade.

Week Content Lecture Notes Jupyter Notes
Markus Grasmair Helge Holden & Elisabeth Köbis .ipynb .pdf
Introduction to Jupyter notebooks and python for numerical analysis Introduction I
Introduction II
Cascade Style Sheet
41 Mathematical preliminaries. Numerical methods for nonlinear equations. Forelesning 15 Slides - 6. oktober
Forelesning 16 Slides - 9. oktober
lecture_15.pdflecture_16.pdf Preliminaries
Nonlinear equations
Preliminaries
Nonlinear equations
42 Numerical methods for nonlinear equations, polynomial interpolation Forelesning 17 Slides - 13. oktober
Forelesning 18 Slides - 16. oktober
Lecture - Oct 12 lecture18.pdflecture18_additional.pdf Polynomial interpolation Polynomial interpolation
43 Numerical integration Forelesning 19 Slides - 20. oktober
Forelesning 20 Slides - 23. oktober
lecture_19.10.2020.pdflecture_23-10-2020.pdf Numerical quadrature Numerical quadrature
44-45 Numerical solution of ordinary differential equations Forelesning 21 Slides - 27. oktober
Forelesning 22 Slides - 30. oktober
Forelesning 23 Slides - 3. november
Forelesning 24 Slides - 6. november
lecture_20201026.pdflecture_30-10-20.pdf
forelesning_20201102.pdf lecture_20201106.pdf
Numerics of ODEs

Stiff ODEs
Numerics of ODEs

Stiff ODEs
46 Numerical differentiation and numerical solution of partial differential equations Forelesning 25 Slides - 10. november
Forelesning 26 Slides - 13. november
lecture_25.pdf lecture_26.pdf Numerics of PDEs Numerics of PDEs
47 Revision Forelesning 27 Slides - 17. november
Sammendrag
Spørretime
reviewlecture.pdfold_exam_questions.pdf

There are video lectures from 2011, which should only be considered as support, and not as replacement of the class lectures. Note that the order in which the different topics were discussed in 2011 differs from the lectures, the curriculum has also been altered, in particular the numerics part.

2020-11-23, Markus Grasmair