| TTIT46 | Mathematical tools, 10,5 ECTS-points /Tema 1: Matematiska verktyg/ Advancement level: B | |
| Aim: Understanding of mathematical models for random phenomena. Ability to analyse the models and to find models for experimental results , i.e. to apply probability theory in practical situations. Knowledge about and understanding of analysis of linear systems. Ability to interpret properties of signals. Knowledge about the dependence between output and intput of a linear system.Prerequisites: Mathematics from year 1. Theme 1 from year 1 semester 2.Course organization: See the study handbook.Course content: The concept of probability, conditional probability, combinatorics. Random variables and their distributions.The joint distribution of two or more random variables; random processes. Expected value, varians, covarians, correlation. One dimensional and multi dimensional normal distribution. Estimation of parameters for the normal, binomial and Poisson distributions. Description av periodic signals; mean values, fourier series, spectral analysis. Analysis of linear systems with periodic signals as input. Description of general deterministic signals using fourier transform, spectral analysis. Calculation of the output from a linear system using the fourier transform, frequency function. Description of linear systems with the impulse response. Calculation of the system output using convolution. The use of laplace transform for system analysis, system function.Course literature: See literature list. | ||