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Kort version - Fuld version
Anvendt Matematik 2 (Efterår 2011) |
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| Kursuskode : | M-MAT2-U1 | ||
| ECTS Point : | 5 | Status : | Obligatorisk |
| Revideret : | 22/02 2011 | Oprettet : | 28/01 2010 |
| Placering : | 4. semester | Timer pr. uge : | 4 |
| Længde : | 1 semester | Undervisningssprog : | Dansk |
| Målsætning : | To provide the participants with both an intuitive and rigorous understanding of probability theory, and to give them an introduction to statistical thinking and methods. This is partly done by exposure to a number of basic probabilistic/ statistical models of widespread application. Important statistical principles for collection and analysis of data are introduced, and methods for model choice, estimation, testing and model verification are presented. The participants learn to handle a number of elementary problems which occur frequently in engineering practice and are thus enabled to critically assess statistical (empirical) investigations and references. This enables the participants to discuss a given scientific method and the possibility to follow a research and development effort. A student who has met the objectives of the course will be able to: • Apply basic definitions and axioms of probability in problem solving. • Formulate simple probability models from verbal descriptions. • Identify and describe probability distributions, including Poisson, binomial, exponential and the normal distribution. • Choose a suitable probabilistic model for a real world phenomenon based on the characteristics. • Estimate and interpret simple summary statistics, such as mean, standard deviation, variance, median and quartiles. • Apply simple graphical techniques, including histograms and box plots. • Compare different statistical methods. • Apply and interpret important statistical concepts, such as the formulation of models, parameter estimation, construction of confidence intervals and hypothesis testing. • Apply and interpret simple statistical methods within one- and two sample situations. • Apply and interpret simple statistical methods within simple linear regression and analysis of variance. • Understand and interpret output from some commonly used statistical software, currently Minitab. • Perform sample size calculations in simplified and standard setups. • Debate and criticize empirically based information. |
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| Hovedindhold : | Axioms of probability theory, conditional probability, independence, Bayes" rule, the binomial distribution, normal approximation to the binomial distribution, sampling with and without replacement, the hypergeometric distribution, discrete random variables, moments with emphasis on mean value and variance, the geometric and negative binomial distributions, the Poisson distribution, continuous random variables, the normal, exponential, and gamma distributions, cumulative distribution function, the chi-squared distribution, the central limit theorem. Simple methods for graphical and tabular assessments of collected or measured data. Hypothesis testing, estimation of parameters, and construction of confidence intervals in common situations (especially mean values, variances, and proportions). Introduction to regression analysis and analysis of variance. Model formulation. Model control: goodness-of-fit test and test for independence. Applications of Minitab in the above areas. Examples of applications in the engineering sciences. |
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| Undervisningsform : | The teaching is problem-oriented, based on examples from the engineering sciences. There will be introductory and summing up lectures. Project work in small groups includes computer simulations, use of internet search engines and case studies | ||
| Krævede forudsætninger : | Applied Mathematics 1 or equivalent. | ||
| Relationer : | Applied Mathematics 1, Project 4 and Theory of Science, Ethics & Aesthetics for Engineers. | ||
| Prøveform : | Skriftlig 4-timers prøve | ||
| Censur : | Ekstern | ||
| Bedømmelse : | 7-trinsskala | ||
| Bemærkninger : | This course is an integrated part of the study program “Engineering Design & Industrial Innovation” offered by the Department of Mechanical Engineering. It is, however, a general methodological course aimed at all engineering students, regardless of specialization. | ||
| Undervisningsmateriale : | - Probability & Statistics for Engineers & Scientists: International Edition, by R. E. Walpole, R. H. Myers, S. L. Myers, K. Ye, Pearson 2007, and - MINITAB Release 14 for Windows CD. Package ISBN: 9781408230916. - Lecture notes on CampusNet. |
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| Ansvarlig underviser : | Imad Abou-Hayt
, iabo@dtu.dk |
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