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Applied Mathematics 2 (Spring 2011) |
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| Course code : | ME-MAT2-U1 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Revised : | 22/02 2011 | Written : | 16/07 2009 |
| Placement : | 4. semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | English |
| Objective : | 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. The course gives the mathematical background for probabilistic methods used in stochastic processes and in statistics. The participants aalso learn to handle a number of elementary problems which occur frequently in engineering practice and are thus enabled to critically assess probabilistic and statistical (empirical) investigations. 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. • Apply the concepts of conditional probability and conditional distribution. • 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. • Perform calculations involving distributions, expectations, moments and correlations. • Estimate and interpret simple summary statistics, such as mean, standard deviation, variance, median and quartiles. • Apply simple graphical techniques, including histograms and box plots. • Apply and interpret important statistical concepts, such as the formulation of models, parameter estimation, construction of confidence • Understand and interpret output from some commonly used statistical software. |
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| Principal Content : | Axioms of probability theory, elements of combinatorial analysis, conditional probability, independence, Bayes" rule, random variables, expectation, the binomial distribution, normal approximation to the binomial distribution, sampling with and without replacement, the hypergeometric distribution, the geometric and negative binomial distributions, the Poisson distribution, cumulative distribution function, the normal, exponential, and gamma distributions, the chi-squared distribution, random number generation, Markov and Chebychev inequalities, generating functions, law of large numbers, functions of random variables, joint distributions, 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. Model formulation. Model control: goodness-of-fit test and test for independence. Examples of applications in the engineering sciences. |
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| Teaching method : | 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 tutorial exercises, computer simulations and case studies | ||
| Recommended prerequisites : | - | ||
| Relations : | Applied Mathematics 1and Theory of Science, Ethics & Aesthetics for Engineers. | ||
| Type of examination : | Four hours written examination | ||
| External examiner : | External | ||
| Marking : | 7 step scale | ||
| Remarks : | The final evaluation of each student will be based on a four-hour written exam. A number of assignments should be submitted and approved in order to be eligible to take the exam. The assignments can be submitted groupwise. 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. |
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| Teaching material : | Lecture notes on CampusNet. |
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| Responsible teacher : | Imad Abou-Hayt
, iabo@dtu.dk |
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