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Applied Mathematics 1 (Fall 2011) |
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| Course code : | ME-MAT1-U1 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Revised : | 13/07 2010 | Written : | 26/01 2009 |
| Placement : | 2. semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | 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 : | Linear equations. Matrix algebra. Eigenvalue problems. Complex numbers. Functions of one real variable: Engineering applications of differentiation and integration. First and second order differential equations. Functions of several real variables: Partial derivatives and linear approximations. Applications of MathCAD in the above areas. Examples of applications in the engineering sciences. | ||
| Teaching method : | The teaching is based on “learning by doing”. There will be introductory and summing up lectures. Students work in small groups with problem solving, computer simulations and case studies. | ||
| Relations : | Projects 2-4, Applied Mechanics 1 & 2 and Applied Mathematics 2. | ||
| 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 : | 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 |
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