MEK2000 Mathematics 2000 Course description

Oral exam, 30 minutes per student.

The oral exam cannot be appealed.

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

None.

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 converge, with emphasis on Taylor and Fourier series
• differentiate and integrate power series term by term
• explaining what a frequency spectrum is and explaining the principle of filtering signals in the frequency domain
• 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
• explaining partial differentiation and using different graphical ways to describe and visualize functions of two variables
• calculating eigenvalues and eigenvectors of matrices and giving geometrical interpretations of these values

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
• discussing error bounds when using Taylor polynomials to approximate functions
• using simple tests of convergence of series, for example the ratio test
• giving a geometrical interpretation of gradient and directional derivative and using linear approximation and total differential of functions of two variables to calculate uncertainty
• using partial differentiation optimize functions of two variables
• using eigenvalues and eigenvectors to solve systems of differential equations with constant coefficients

General competence

The student is capable of:

• identifying the connection between mathematics and their own field of engineering
• translating a practical problem from their own field into mathematical form, so that it can be solved analytically or numerically
• using mathematical methods and tools that are relevant to their field of engineering
• assessing the results of mathematical calculations and using basic numerical algorithms

Two sensors, one from the teaching staff, the other may be internal or external. External examiner is used periodically.

Basic background in computer science and networking.

The course describes the important enabling technologies of cloud computing, explores state- of-the art platforms and existing services, and examines the challenges and opportunities of adopting cloud computing. Moreover, the course investigates how to protect the critical data increasingly being stored in the cloud. The students learn how to build a security strategy that keeps data safe and mitigates risk.

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.