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Applied Mathematics 1 (Spring 2013) |
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| Course code : | ME-MAT1-U1 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Revised : | 22/03 2013 | Written : | 26/01 2009 |
| Placement : | 1. semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | Danish and English |
| Objective : | To provide the students with basic knowledge in the fundamental tools for constructing and analyze mathematical models, and to provide a basis for further studies in modern engineering mathematics. The use of computer software supports both of these aspects. A student who has met the objectives of the course will be able to: • Apply matrix algebra and Gaussian elimination to solve systems of linear equations. • Use vectors to solve engineering problems. • Apply differentiation and integration to engineering problems. • Analyse simple mathematical models. • Find lengths, areas and volumes of geometrical entities. • Solve simple first order and second order differential equations. • Use the algebraic and geometric representations of complex numbers and the complex exponential function. • Find partial derivatives and linear approximation. • Determine extrema for functions of several variables. • Use computer software, currently MathCAD, for the solution and the graphical illustration of mathematical problems. • Read engineering literature on applied mathematics. |
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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. The Laplace Transform. Examples of applications in the engineering sciences. | ||
| Teaching method : | The pedagogy of the course is “problem-based learning”. Some of the time allocated to the course will be used in working with guided assignment. The course assignments 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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| Required prequisites : | None | ||
| Recommended prerequisites : | None | ||
| Relations : | The course is fundamental to the whole study programme in mechanical engineering. | ||
| Type of examination : | Four hours written examination | ||
| External examiner : | External | ||
| Marking : | 7 step scale | ||
| Remarks : | 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. | ||
| Teaching material : | Engineering Mathematics Through Applications, ISBN-13: 9780333922248, by Kuldeep Singh, Palgrave Macmillan 2003. - Lecture notes on CampusNet. |
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| Responsible teacher : | Imad Abou-Hayt
, iabo@dtu.dk Ole Remmer , olre@dtu.dk Rasmus Post , rapo@dtu.dk |
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