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Mathematics and Modeling III (Spring 2013) |
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| Course code : | ME-MAM3-U1 | ||
| ECTS Credits : | 10 | Status : | Compulsory |
| Revised : | 29/01 2013 | Written : | 29/03 2012 |
| Placement : | 3. & 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. In addition, The course gives an introduction to numerical analysis, optimization techniques and operations research, as well as their applications in engineering practice. A student who has met the objectives of the course will be able to: • 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 and interpret important statistical concepts, such as the formulation of models, parameter estimation, construction of confidence intervals and hypothesis testing. • Apply optimization techniques to solve engineering problems. • Formulate linear and nonlinear programming models from verbal description. • Solve and interpret linear and nonlinear programming models. • Use numerical analysis to solve engineering problems, using computer software. • Use computer software and graphing calculators for the solution and the graphical illustration of mathematical problems. • Apply the topics of the lectures to practical problems through project work in groups. • Learn new topics in engineering mathematics through guided projects. • Organize project work in small groups. • Write a professional project report containing the mathematical analysis and the solutions of the problems posed in the assignments. |
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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. 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. Introduction to operations research and linear programming. Simplex methods. Optimization techniques and nonlinear programming. Introduction to numerical analysis. Examples of applications in the engineering sciences. | ||
| Teaching method : | The pedagogy of the course is “problem-based learning”. Approximately half of the time allocated to the course will be used in guided project work in groups. The course projects will give the students an opportunity to apply basic concepts learned in the class to real-life problems, and to learn new topics in mathematics that are not covered in the lectures. There will be introductory and summing up lectures and students will work in small groups with projects, problem solving, computer simulations and case studies. |
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| Required prequisites : | ME-MAM2 or equivalent. | ||
| Relations : | ME-MAM1 and ME-MAM2. The course is otherwise fundamental to the whole study program in mechanical engineering. | ||
| Type of examination : | Look under remarks | ||
| 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 group project assignments should be submitted and approved in order to be eligible to take the exam. 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 : | - Probability and Statistics for Engineers and Scientists, International edition, 9th edition, ISBN-13: 9780321748232, Pearson. - Lecture notes on CampusNet. |
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| Responsible teacher : | Imad Abou-Hayt
, iabo@dtu.dk |
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