Module A1.1 - Mathematical Methods

1

Matrices I
Vector Space, Span, Basis vectors, Linear Operators, Matrices

2

Matrices II
Properties of Matrices, special Matrices, Trace, Determinant

3

Matrices III
Determinant, Inverse

4

Matrices IV
Matrices in Optics: Translation, Refraction, thin Lenses, Rank of a Matrix

5

Matrices V
Simultaneous linear Equations: Gaussian Elimination Direct Inversion, LU Decomposition, Cramer's rule; Eigenvalues and Eigenvectors

6

Fourier Series I
Dirichlet Conditions, orthogonal relations, Fourier-coefficients

7

Fourier Series II
Complex Fourier series, Examples

8

Fourier Series III; Fourier Transformation I
Parseval's theorem; Fourier Transformation, properties

9

Fourier Transformation II
Properties, Delta-distribution

10

Fourier Transformation III; Ordinary differential Equations I
Convolution and Parseval's theorem; Examples, classification

11

Ordinary differential Equations II
Geometrical representation, seperable differential eqations

12

Ordinary differential Equations III

13

Ordinary differential Equations IV
Exact differential equations