# Lecture plan

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

#### Laplace transforms and Fourier analysis.

The chapter numbers refer to the 10th edition of Kreyszig.

Week Chapter Content
34 6.1, 6.2 Laplace transforms, transform of derivatives, ODE
35 6.3 - 6.5 Heaviside function, delta function, convolution
36 6.6, 6.7, 11.1 More ODEs, Fourier series (lecture notes 1) and (lecture notes 2)
37 11.2 - 11.4 Fourier series: representations and convergence (lecture notes 3) and (lecture notes 4)
38 11.7, 11.9 Fourier integral and transform (lecture notes 5) and (lecture notes 6)
39 12.1 - 12.4 Wave equation (lecture notes 7) and (lecture notes 8)
40 12.5 - 12.7 Heat equation (lecture notes 9) and (lecture notes 10)

Pang's TMA4130 Part I Notes Not everything here was in lectures, and not everything said in lectures is included here, and non-examinable material are marked as such.

#### Numerical methods.

The curriculum is covered by the notes found in Jupyter notes — also found below. There are also pdf-versions of the notes available. Jupyterhub is used for running/viewing the .ipynb files, and can be accessed via this link: (Jupyterhub). You can also use the .ipynb files by downloading Jupyter Notebook here, or with Python here if you do not already have Python.

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 Notes Jupyter Notes
41 Introduction to numerical methods.
Polynomial interpolation (lecture notes 11) and (lecture notes 12)
Preliminaries.pdf , PolynomialInterpolation.pdf .ipynb, .ipynb
42 Numerical integration (lecture notes 13) and (lecture notes 14) Quadrature.pdf .ipynb
43 Numerical solution of nonlinear equations (lecture notes 15) and (lecture notes 16) NonlinearEquations.pdf .ipynb
44 Numerical solution of ordinary differential equations (lecture notes 17) and (lecture notes 18) ODEs.pdf, StiffODEs.pdf .ipynb, .ipynb
45-46 Numerical differentiation and numerical solution of partial differential equations (lecture notes 19), (lecture notes 20), (lecture notes 21) PDEs.pdf .ipynb
47 Revision (lecture notes 22)

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. Holden's lectures are being video recorded (requires login).