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| TAIU30 | Mathematics, B. Sc. Course, 3 p (sw) /Flervariabelanalys/ Advancement level: B | |
| Aim: To give the student familiarity with several variable calculus such as is used in technical subjects. Further, the course will teach the student to understand and exploit basic probability theory and statistics, that is the theory of trials which are influenced by chance factors.Prerequisites: Mathematics (TNDE 20, TNEI 40, TAEI 40, TADI 30, or TAMI 20, TAIU 21 and TNDE 21).Supplementary courses: TATM 96 Vector Analysis, B. Sc. course.Course content: Mathematical statistics: Event space, events and probabilities. Combinatorics. Conditional probability and independent events. Stochastic variables, their probability distributions, expectation values and standard deviations. In particular, the exponential, normal, binomial and Poisson distributions are considered. Descriptive statistics. Point estimation of expectation values and standard deviation. Normal distribution paper. Confidence intervals for random testing from a normal distribution and a binomial distribution. -test. Simple linear regression. Several variable calculus: Functions of several variables. Partial derivatives, chain rule and error propagation. Taylors formula and local extrema. Largest and least values. Optimisation with constraints. Double and triple integrals. Change of variables in multiple integrals.Course literature: Jonsson, Dag, Norell, Lennart: Ett stycke statistik. Uppsala University. Persson, Arne, Böiers, Lars-Christer: Analys i flera variabler. Studentlitteratur, Lund 1988. | ||
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