BYPE2000 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 BYFE1000 - Mathematics 1000.

No requirements over and above 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 power series, explain what it means that a series converge, and differentiate and integrate powerseries.
• describe the Laplace transform and know about its basic properties
• describing and explaining how a sequence of numbers can originate by sampling, by using a 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 functions of two variables
• calculating eigenvalues and eigenvectors of matrixes and giving a geometrical interpretaions of these values

Skills

The student is capable of:

• discussing pro and cons using interpolating polynomials, splines and least squares method to interpolate sampled data
• discussing error barriers when using 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
• using partial differentiation to calculate and classify critical points of functions of two variables
• use the Laplace transform to solve simple ordinary differential equations
• using eigenvalues and eigenvectors to solve systems of differential equations with constant coeffisients 

General competence

The student is capable of:

• assessing the results of mathematical calculations
• write precise explanations and justifications to approaces, and demonstrate correct use of mathematical notation
• using mathematical methods and tools that are relevant to their field of engineering
• 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

Joint lectures and exercise sessions. In the exercise sessions, the students work on assignments, both individually and in groups, under the supervision of a lecturer.

None.

Individual written exam, 3 hours

The result of the exam can be appealed.

A handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator's internal memory can store data, the memory must be deleted before the exam. Random checks may be carried out.

All printed and written aids.

Grade scale A-F.

One internal examiner. External examiners are used regularly.