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Mathematics and Modeling II (Efterår 2011) |
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| Kursuskode : | ME-MAM2-U1 | ||
| ECTS Point : | 10 | Status : | Obligatorisk |
| Revideret : | 18/10 2011 | Oprettet : | 18/10 2011 |
| Placering : | 2. semester | Timer pr. uge : | 8 |
| Længde : | 1 semester | Undervisningssprog : | Engelsk |
| Målsætning : | To provide the students with basic knowledge in fundamental mathematical tools to solve engineering problems and to construct and analyze mathematical models, as well as to provide a foundation for further studies in modern engineering mathematics. The use of computer software and graphing calculators supports both of these aspects. A student who has met the objectives of the course will be able to: • Apply linear algebra to solve engineering problems. • Use matrices and determinants to solve systems of linear equations. • Determine partial derivatives, extreme values and gradients. • Use Lagrange multipliers to solve optimization problems. • Calculate double and triple integrals. • Calculate line and surface integrals. • Use Green’s theorem and Stokes’ theorem in vector fields. • Use vector analysis to model and solve practical engineering problems. • 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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| Hovedindhold : | Introduction to linear algebra: Matrices, determinants, systems of linear equations, eigenvalues and eigenvectors. Functions of several variables: Partial derivatives and multiple integrals, extreme values, Lagrange multipliers. Vector analysis: Line integrals, conservative fields, Green’s theorem, surface integrals, Stokes’ theorem. Examples of applications in the engineering sciences. | ||
| Undervisningsform : | 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 concepts 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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| Krævede forudsætninger : | ME-MAM1 or equivalent. | ||
| Anbefalede forudsætninger : | None | ||
| Relationer : | ME-MAM1 and ME-MAM3. The course is otherwise fundamental to the whole study program in mechanical engineering. | ||
| Prøveform : | Se under bemærkninger | ||
| Censur : | Ekstern | ||
| Bedømmelse : | 7-trinsskala | ||
| Bemærkninger : | The evaluation of each student will be based on a four-hour written exam, worth 50% of the final grade, and on a number of project assignments throughout the semester. A final group report containing the assignments should be submitted at the end of the semester. The group report is worth 50% of the final grade. 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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| Undervisningsmateriale : | - Thomas" Calculus, Global Edition, 12th Edition, by George B. Thomas, Maurice D. Weir, and Joel Hass. ISBN-13: 978-0-321-64363-6, Pearson 2010. - Lecture notes on CampusNet. |
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| Ansvarlig underviser : | Imad Abou-Hayt
, iabo@dtu.dk |
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