Lecture plan
This is a tentative schedule, which will be updated continuously.
The chapter numbers refer to the 10th edition of Kreyszig.
The video lectures refer (approximately) to the 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. Also, there will probably be small differences in content. That is, it is possible that some of the topics discussed in 2011 will not be part of this year's lecture and vice versa. Be aware of these differences in particular when preparing for the exam!
| Week | Chapter | Content | Video Lectures and notes |
|---|---|---|---|
| 02 | 11.1 | Introduction. Periodic functions, trigonometric series, Fourier series. Euler's formula. Convergence of the Fourier series. | 10, 11, 12 |
| 03 | 11.2-11.4 | Changes of the period. Symmetries, cosine and sine series. Application: "Forced oscillations." Approximation by trigonometric polynomials, Parseval's identity. | 13, 14, 16, 17 |
| 04 | 12.1-12.3 | Partial differential equations (PDEs). Vibrating String, Wave equation. Separation of variables. | 24, 26, 27, 28, 29 |
| 05 | 12.4, 12.6 | D'Alembert's solution of the one-dimensional wave equation. Heat equation. Steady 2D Heat problem and Laplace equation. | 29, 30, 26, 27, 28, 31 |
| 06 | 11.7, 11.9 | Complex Fourier series. Fourier real and complex integral, Fourier Sine and Cosine integral. Fourier transform, Convolution. | 19, 20, 21, 22, 23 |
| 07 | 12.7, 6.1-6.2 | Solution of the heat equation using the Fourier transform. Laplace transform, existence, uniqueness and properties, shifting theorem, transforms of derivatives and integrals. | 31, 32, 2, 3, 4 |
| 08 | 6.2-6.6 | Laplace transform, solving ODEs, unit step function, shifting theorems, modelling circuits, short impulses and Dirac Delta functions, convolution and Integral equations. Differentiation and integration of transforms. | 4, 5, 6, 7, 8, 9, 10 |
| 09 | Bruk av Jupyter. Numerisk løsning av ikkelineære ligninger. | Introduksjon.ipynb, Introduksjon.pdf, IkkeLineareLigninger.ipynb, IkkeLineareLigninger.pdf | |
| 10 | Polynominterpolasjon. | Polynominterpolasjon.ipynb, Polynominterpolasjon.pdf | |
| 11 | Numerisk integrasjon. | Integrasjon.ipynb, Integrasjon.pdf | |
| 12 | Numerisk løsning av ordinære differensialligninger. | OrdinareDifferensialligninger.ipynb, OrdinareDifferensialligninger.pdf | |
| 13 | Påskeferie | ||
| 14 (onsdag) | Numerisk løsning av stive ordinære differensialligninger. | StiveODL.ipynb, StiveODL.pdf | |
| 15 | Numerisk derivasjon Numerisk løsning av to punkts randverdiproblem | Derivasjon.ipynb, Derivasjon.pdf, ToPunktRandverdiproblem.ipynb, ToPunktRandverdiproblem.pdf | |
| 16 | Numerisk løsning av partielle differensialligninger / Repetisjon | PartielleDifferensialligninger.ipynb, PartielleDifferensialligninger.pdf | |
| 17 (tirsdag) | Repetisjon |