TNDE23	Statistics and transforms, 6 ECTS-points /Statistik och transformer/ Advancement level: B
	Aim: The course in statistics will teach the student to understand and use fundamental prohability theory and statistics, i.e. the theory for experiments influenced by random factors. The course in transforms will give knowledge about mathematic methods used to solve problems in circuit theory, automatic control and signal processing Prerequisites: Elementary calculus, algebra, especially integrals, derivatives, power series and differential equations. An approriate course is TNDE 21 Supplementary courses: TNIU 54, TNIU 56 Course organization: Two main parts, consisting of a course statistics and transforms. The teaching consists of lectures followed by lessons with problemsolving guided by a teacher. Course content: Statistics: Introduction to fundamental concepts of probability theory. Combinations. Conditional probabilities and independent events. The concept of a stochastic variable and its frequency function. The expectation and variance of a stochastic variable. Some important distributions such as the exponential, normal, binomial and Poisson distribution. The central limit theorem. Statistical techniques and tables. Graphic presentation. Measures of location and dispersion. Estimations of expectation and variance. Confidence intervals. Chi-square distributions. Regression analysis. Gauss' theorem. Transforms: Fourier series of periodic functions. The Fourier transform and the Fourier integral. An introduction to step- and impulse functions. Definition of the one-sided Laplace Transform. How to solve differential equations using the Laplace Transforms. Definition of the one-sided Z-Transform. How to solve difference equations using the Z-Transform. Course literature: Jonsson, Dag and Norell, Lennart: Ett stycke statistik Kompendium i statistik, produced by the institution Kompendium om transformer, produced by the institution.
TEN1	Written examination, 4 p.

Course language is swedish.