## Files for the Lab Sessions

The files for the local laboratories are in this directory .

## Analysis 1

Topics:

• Equations, functions, mappings
• Polynomials, rational functions, trigonometric functions, exponential and logarithmic functions
• Sequences, continuity
• The derivative and its applications

Find the complete lecture notes for this class in either french or german as a PFD file.

## Analysis 2

Topics:

• The integral and its applications
• Curves and line integrals
• Calculus in multiple variables

Find the complete lecture notes for this class in either french or german as a PFD file.

## Linear Algebra and Geometry

Topics:
• Numbers and Proofs
• Complex Numbers
• Vectors and Matrices
• Systems of linear Equations
• Matrices and LU factorization
• Determinants
• Lineare Structures
• Linear Mappings
• Applications

Find the complete lecture notes for this class in either french or german in the PFD format. A short summary of the content of the class is given in overview .

## Mathematics 1, Differential Equations and Laplace Transforms

Find the rules for this module in the Merkblatt.

Topics:

• Ordinary differential equations, the basics
• Laplace transform, the basics
• Applications of the Laplace transform
• Ordinary differential equations, numerical approches and systems of equations

Find the current version of the lecture notes for this class as a PFD file.

## Mathematics 2, Fourier Methods and Applied Statistics

As introduction to Fourier methods examine the note DemoDay.pdf. In this short note the two Matlab/Octave codes Phasor.m and AudioSpectrumAnalyzerDezibel.m are used.

This module consists of two courses: Fourier Methods and Applied Statistics. Find the rules for this module in the Merkblatt.

### Fourier Methods

Topics:

• Fourier series, the basics, real and complex notation,
• Properties, convolution
• DFT, FFT, windowing
• Applications, boundary value problems
• Fourier transform, basics and applications

Find the current version of the lecture notes for this class as a PFD file.

### Applied Statistics

The course is using the lectures notes by Prof. Roger Filliger, available as PDF: Angewandte Statistik.

Throughout the class Octave and/or Matlab will be used. You will need a laptop with a working copy of Octave or Matlab. For Matlab you will need the Statistics Toolbox and for Octave the package Statistics. Since there are (too) many commands I created a short document with the commands useful for statistics, available at Statistics with Matlab/Octave. This document will be updated during the semester.

Many data sets will be used to test the results and apply the algorithms. Find the data files and sample codes in the directory Data_Files.