MEK2000 Mathematics 2000 Course description

This course, together with Mathematics 1000, will give the students an understanding of mathematical concepts, problems and solution methods with the focus on application, particularly in engineering subjects.

The course builds on ELFE/MAFE/KJFE1000 Mathematics 1000 or MEK1000.

There are no requirements beyond the admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student is capable of:

• explaining how functions can be approximated by Taylor polynomials and truncated Fourier series,
• explain what it means that a series converges, with emphasis on power and Fourier series,
• differentiating and integrating power series term by term,
• explaining what a frequency spectrum is,
• describing and explaining how a sequence of numbers can originate by sampling, by using formulae or as the solution of a difference equation,
• explaining how to interpolate sampled data,
• explain linear regression based on sampled data,
• explaining partial differentiation and using using relevant tools visualize functions of two variables,
• calculating eigenvalues and eigenvectors.

Skills

The student is capable of:

• discussing the connection between Fourier series and the Fourier transform,
• discussing pros and cons using interpolating polynomials, and splines to interpolate sampled data,
• explaining how the method of least square may be applied to fit data to a linear function and implement such methods numerically on for larger data sets,
• discussing error bounds when using Taylor polynomials to approximate functions,
• using simple tests for convergence of series,
• giving a geometrical interpretation of gradient and directional derivative and using linear approximations of multi variable functions,
• using partial differentiation optimize functions of two variables - both analytically and by implementing the method of gradient ascent/descent,
• using eigenvalues and eigenvectors to solve coupled linear systems of differential equations with constant coefficients.

General competence

The student is capable of:

• identifying connections between mathematics and their own field of engineering,
• translating practical problems, preferably from their own field, into mathematical form so that it can be solved analytically or numerically,
• assessing her or his own results from analytical and numerical calculations,
• formulating precise explanations, providing justifications for the choices of methods and demonstrating correct use of mathematical notation,
• using relevant analytical and numerical methods and tools,
• use mathematics to communicate problems and solutions within engineering sciences.

The course is taught through joint lectures and exercises. In the exercise sessions, the students work on assignments, both individually and in groups, under the supervision of a lecturer. These sessions will also involve assessing the assignments - both own ones and assignments carried out by fellow students.

Also in between teaching sessions, the students are expected to work with exercises. The proposed exercises are directly linked to learning outcomes for the course. Assessing their own and others' solutions will provide the students with insight as to which extent these goals are achieved.

The students will also have the option of handing in certain exercise sets and have these assessed.

None.

Individual written exam under supervision, 3 hours.

The exam result can be appealed.

All printed and written aids.

Calculator.

Grade scale A-F.

One internal examiner. External examiners are used regularly.

The course has an overlap of 10 credits with MAPE2000, KJPE2000, EMPE2000 and BYPE2000. This course overlaps 5 credits with DAPE2000 and ELTS2000. Under the rule that students have three attempts to take an exam, attempts in equivalent courses also count.