# Lecture plan

This section contains the material covered in class, and thus, which will be evaluated on the exam. Everything that was covered in class or in the exercises is material for the exam.

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
34 11.1 Introduction. Periodic functions, trigonometric series, Fourier series. Euler's formula. Convergence of the Fourier series. 10, 11, 12
35 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
36 12.1-12.3 Partial differential equations (PDEs). Vibrating String, Wave equation. Separation of variables. 24, 26, 27, 28, 29
37 12.4, 12.6 D'Alembert's solution of the one-dimensional wave equation (no method of characteristics). Heat equation. Steady 2D Heat problem and Laplace equation. 29, 30, 26, 27, 28, 31
38 11.7, 11.9 Complex Fourier series. Fourier real and complex integral, Fourier Sine and Cosine integral. Fourier transform, Convolution. (no DFT, FFT). 19, 20, 21, 22, 23
39 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
40 6.2-6.5 Laplace transform, solving ODEs, unit step function, shifting theorems, modelling circuits, short impulses and Dirac Delta functions, convolution and Integral equations. 4, 5, 6, 7, 8, 9
41 6.6; 19.1-19.2 Laplace transform, differentiation and integration of transforms. Numerical analysis, error, significant digits. Fixed point iterations for the solution of non-linear equations. Newton's method in one dimension. 10, 33, 34
42 19.2-19.3 Convergence order. Secant method. Newton's method in higher dimensions (notes in "some lecture notes" section). Lagrange Interpolation. 35, 36, 37
43 19.3, 19.5 Newton's divided difference (no equal spacing ). Chebyshev points (notes in "some lecture notes" section). Numerical integration (no numeric differentiation). 37, 38, 39, 40, 41
44 20.1-20.3 Numerical solution of linear equations: Gauss elimination and Back substitution, LU factorization, Jacobi method, Gauss-Seidel method, Convergence (+ Strict diagonal dominance). 41, 42, 43, 44, 45
45 21.1, 21.3 Numerical solution of ODEs: Euler method and improved Euler method. Convergence order, RK methods, Backward Euler method, Systems and higher order equations. 44, 45, 46, 47, 48
46 21.4, 21.6 Numerical solution of PDEs: Methods for Elliptic (no ADI method) & Parabolic PDEs, Crank-Nicolson Method. 48, 49, 50, 51
47 Repetition