EMPE2000 Mathematics 2000 Course description

The coursework will give the students insight into areas of mathematics that are important when modelling technical and natural science systems and processes. The subjects covered are included in engineering programmes the world over and are necessary to effective and precise communication between engineers. Students will practise using mathematical software in the work on the course, which will enable them to carry out calculations in a work situation.

The course builds on EMFE1000 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:

• describing and explaining how sequences can be derived through sampling (measurement), with the use of formulas, and to solve differential equations
• explaining the interpolation problem, and using methods of polynomial and spline interpolation
• explaining the method of least squares for fitting functions to given data
• solving differential equations with constant coefficients of a degree less than or equal to two, both analytically and by simulation
• explaining what is meant by a series and what it means when a series converges
• explaining the Taylor series such as a power series, and differentiating and integrating terms
• calculating Taylor polynomials and calculating the error using the remainder
• explaining how functions can be approximated using Fourier series
• explaining different methods of presenting functions of two variables graphically and discussing the advantages and disadvantages of these methods
• calculating partial derivatives of the first and higher orders
• explaining what the value of the first order partial derivative means
• explaining the geometric interpretation of gradient and directional derivatives
• explaining how to use the extreme value theorem
• explaining what is meant by the differential of a function of two variables
• determining the uncertainty and relative uncertainty of a parameter that depends on several variables

Skills

The student is capable of:

• discussing methods of interpolation and fitting functions
• discussing how functions can be approximated using series
• discussing how a function of two variables can be approximated using a linear function and then used to determine the uncertainty of measurements
• discussing a method for determining and classifying stationary points and determining the extreme values of functions of several variables

General competence

The student is capable of:

• translating a practical problem from his/her own professional field into mathematical expressions, so that it can be solved analytically or numerically
• assessing, for a given problem, whether it is most expedient to decide on an analytical or numerical solution
• assessing the quality of numerical solutions, for example by calculating error bounds or by comparisons with analytical solutions
• using the programming elements assignment, for loops, if testes, while loops etc. for solving mathematical problems numerically
• assessing his/her own academic work and that of other students, and formulating written and oral assessments of these works in an academically correct and precise manner
• writing precise explanations and reasons for using procedures, and demonstrating the correct use of mathematical notations

Teaching is organised as scheduled work sessions, during which the students complete exercises in the subject matter presented ('lectured'). The exercises include solving problems, discussions, collaboration and individual work. Use of numerical software will be included.

In the scheduled work sessions, the students will be offered to participate in 'peer assessment'. This means that the students assess each other's work and give feedback to promote learning.

Between the scheduled work sessions, the students must work individually and/or in groups on calculation exercises and practical use of numerical software.

None.

Individual home exam, 5 hours.

The exam result can be appealed.

All aids allowed.

Grade scale A-F.

One internal examiner. External examiners are used regularly.