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.

Pass/fail.

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

The goal of the course is to give students real-life problems and research advancements in the topic, and a more comprehensive understanding of what the design of complex structures involves. Through seminars with contribution from invited researchers and experts from the consulting industry, students will be presented a wide range of topical issues relating to the analysis and design of large structures such as bridges, offshore installations, high-rise buildings, building physics, new building materials, transport infrastructure etc.

A project assignment is also included to give the students both theoretical knowledge and experience of applying this knowledge to real-world complex issues. The assignment shall be based on a real building and construction project or be part of a more extensive research and development project, and the project report shall take a scholarly, reflective approach to the problem at hand and include a discussion of alternative solutions.

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

·;;;;;;;; has advanced theoretical knowledge of building technology and structural engineering and specialized insight into how to apply the knowledge to a real design issue.

·;;;;;;;; is capable of analyzing a specific topic using scientific work methods.

·;;;;;;;; has developed a comprehensive understanding of what the design of large structures involves.

Skills:

The student is capable of

·;;;;;;;; applying theoretical knowledge to solve real, complex structural engineering problems.

·;;;;;;;; using his/her knowledge to assess and develop more sustainable design solutions.

·;;;;;;;; using analysis tools and methods, and carrying out literature searches to collect, process and present relevant information.

General competence:

The student is capable of:

·;;;;;;;; working in teams and communicating his/her own work.

·;;;;;;;; carrying out a project assignment, including a report and presentation.

·;;;;;;;; preparing a project plan with milestones, and reporting interim results.

The teaching will consist of seminars with invited lecturers, discussions and presentations. The students will be given individual assignments relating to the topics of the seminars (reflection notes) and a bigger; project assignment.

The students must have attended at least 80% of the seminars and have individual reflection notes approved (approx. 4-5 pages per note) linked to the seminars they have attended. Students who fail to meet the coursework requirements can be given up to one opportunity to resubmit reflection notes before the exam.

Portfolio exam which consist of:

Project report prepared individually or in a group of 1-2 students, approx. 20-30 pages, with oral presentation.;

The overall assessment cannot be appealed. If a student fails the project assessment, he/she is given one opportunity to resubmit the project.

All aids are permitted.

Two internal examiners. External examiners are used regularly.