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Mathematics and Modeling 1 (Fall 2011) |
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| Course code : | ME-MAM1-U1 | ||
| ECTS Credits : | 10 | Status : | Compulsory |
| Revised : | 12/08 2011 | Written : | 11/08 2011 |
| Placement : | 1. semester | Hours per week : | 8 |
| Length : | 1 semester | Teaching Language : | English |
| Objective : | To provide the students with basic knowledge in fundamental 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 graphing calculators supports both of these aspects. A student who has met the objectives of the course will be able to: • Apply differentiation and integration to solve engineering problems. • Use power series to approximate functions with polynomials. • Use polar coordinates and parametric equations to solve geometrical problems. • Use vectors and vector-values functions to solve space motion problems. • Find lengths, areas, volumes and centers of mass of geometrical entities. • Use the algebraic and geometric representations of complex numbers and the complex exponential function. • Solve linear first order and second order differential equations. • Use 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 project report containing the mathematical analysis and the solutions of the problems posed in the assignments. |
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| Principal Content : | Applications of derivatives to optimization problems. Applications of definite integrals to lengths, areas, volumes, moments and centers of mass. Infinite sequences and series, including Taylor series. Parametric equations and polar coordinates. Vectors and the geometry of space. Vector-valued functions and motion in space. Complex numbers. First and second order differential equations. Examples of applications in the engineering sciences. | ||
| Teaching method : | The teaching is based on “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, simulations and case studies. |
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| Relations : | The course is fundamental to the whole study program in mechanical engineering. | ||
| Type of examination : | Look under remarks | ||
| External examiner : | External | ||
| Marking : | 7 step scale | ||
| Remarks : | 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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| Teaching material : | 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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| Responsible teacher : | Imad Abou-Hayt
, iabo@dtu.dk |
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