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Numerical Analysis (Spring 2010) |
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| Course code : | ENUMA-U01 | ||
| ECTS Credits : | 7,5 | Status : | Optional for specified Programme |
| Revised : | 26/01 2004 | Written : | 23/04 2002 |
| Placement : | 5-7 semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | English if English students are present |
| Objective : | The purpose of Numerical Analysis is the design of computerbased techniques for the solution of mathematical problems. The focus will be on applications, yet will the theoretical aspects of the material get a good deal of attention in order to establish a solid understanding of problems and methods for solution. | ||
| Principal Content : | Curve Fitting. (Ex: Finding a polynomial expression y = p(x) defining y in terms of x when only a set of samples/measurements (x,y) are given. This is relevant when DC/AC conversion is performed in signal processing.) Interpolation. Ortogonal Polynomials. Splines. Least Squares Regression. Numerical Integration and Differentiation. (Ex: Solving a definite integral when no antiderivative exists. This is relevant for the calculation of probabilities whenever we are dealing with the normal distribution in the processing of random signals.) Trapezoidal Rule Simpson´s Rule Gaussian Quadrature. Richardson Extrapolation. Roots of nonlinear equations. (Ex: Finding the zeros and poles of a transfer function of a filter.) Newton-Raphson for systems of nonlinear equations. Bairstow´s Method. Optimization. (Finding the local minima of a function of several variables. Ex: Design of neural networks.) Conjugate Gradient Methods. Quasi Newton Methods. Ordinary Differential Equations. (Extremely relevant, since only a limi-ted proportion of real-life differential equations have solutions which can be determined by use of classical mathematics.) One Step Methods. Runge Kutta Methods. Multistep Methods. Predictor-Corrector Methods. | ||
| Teaching method : | Lectures, classroom exercises, computerbased assignments. Group Work. | ||
| Required prequisites : | Documented knowledge corresponding to DSM3/DSM4 and OOP1 | ||
| Recommended prerequisites : | LAAF | ||
| Relations : | - | ||
| Type of examination : | Approved labs/assignments | ||
| External examiner : | None | ||
| Marking : | 7 step scale | ||
| Remarks : | A weighted grading of 4 obligatory projects: The first 3 are and defined by the teacher while the 4th may be defined by the student as an individual project.The weighting will be announced in the beginning of the semester. Example explaining the weighted grading:With 2 weeks response time for each of the first 3 projects and 4 weeks response time for the final project weights would be 0.2, 0.2, 0.2, and 0.4. With project grades 10, 8, 9, and 10 the weighted grade obtained for the entire course would be: 0.2*10 + 0.2*8+0.2*9+0.4*10 = 9.4. In this case the final grade is 9.Weights are chosen to reflect the workload of the projects. Weights are announced at the beginning of the semester. Response time for the 3 teacher-defined projects: 2-3 weeks.Response time for the last individual project: 4 weeks.The 4th project is given 4 weeks before the end of the semester, and all lectures during these last 4 weeks are reserved for project work and individual consultation/ coaching.If the student does not wish to define an individual project, one is offered by the teacher. |
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| Teaching material : | Numerical Methods for Engineers. By Chapra & Canale Notes by Agnethe Knudsen, Arly Mencke Hansen & H.C. Pedersen. | ||
| Responsible teacher : | Hans Pedersen
, hchpe@dtu.dk |
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