IRF30017 Mathematics 3 (Autumn 2018)

The course is connected to the following study programs

Optional course in all Bachelor of Engineering programmes.

Absolute requirements

IRF10014 Matematikk 1 or equivalent courses.

Recommended requirements

IRF20014 Matematikk 2 or equivalent courses. 

Lecture Semester

5^th semester (Autumn).

The student's learning outcomes after completing the course

Knowledge:

The student will

• have learned the concepts and terminology related to the course subjects
• be able to follow the logical structure of simple mathematical proofs and derivations
• have good knowledge of calculus with several variables
• have knowledge of the fundamental principles of physics and its scientific method
• have knowledge of how physical laws of mechanics can be applied to model observable phenomena, and have an understanding of the model's range of validity 

Skills:

The student

• has the mathematical and physical prerequisits for a masters programme in engineering
• is able to ressonate and draw logical conclusions
• is able to perform calculations related to the course subjects
• understands and can justify his/her calculations
• is able to apply mathematics to problems in engineering sciences
• is able to use mathematical software for simple simulations
• has quantitative problem solving skills and is able to model by using basic principles from mathematics and physics

Competence:

The student

• understands that the level of precision in mathematics enables structuring of engineering problems and makes these problems solvable
• has gained an understanding of mathematics and physics as a basis for scientific thinking
• is able to communicate with other professionals using mathematical language

Content

Mathematics (70%):

• Conic sections. Quadric surfaces. Parametric curves.
• Functions of several variables. Lagrange multipliers.
• Multiple integrals in two and three dimensions with change of variables.
• Vector fields. Divergence and curl.
• Line and surface integrals.
• Green's, Stokes' and the divergence theorems.

Physics (30%):

• Physics of waves with focus on oscillations, resonance and mechanical waves. Thermal physics with focus on heat transport. The wave equation and the heat equation in one dimension.
• Numerical methods and modeling with applications in physics.
• Use of mathematical software for simulating simple physical systems.

Forms of teaching and learning

Lectures and exercises in plenum plus exercises in workshops. The entire course or parts of it can be completed online.

Workload

250-300 hours

Practical training/internship

None

Coursework requirements - conditions for taking the exam

Up to 13 assignments of which at least one must make use of mathematical software.

Further details of the coursework requirements are given in the semester plan.
All coursework must have been passed and approved before a student may sit the examination.

Examination

Written examination, 4 hours.

Permitted aids:

• Calculator, with empty memory, that cannot compute symbolically and that cannot be used for wireless communication
• One A4 sheet of paper with free content (printed or handwritten, allowed to write on both sides)
• Either Tor Andersen: "Aktiv formelsamling i matematikk" or "Gyldendals formelsamling i matematikk" or a handbook of mathematical formulas in English approved by the teacher prior to the examination
  

The A-F grading system is used, with A as the best mark and F as fail.

Examiners

Two examiners, one internal and one external.

Course evaluation

The course has ongoing evaluation throughout the semester with methods agreed between the teacher (s) and students.

Written final evaluation of the course.

Literature

Hass, J.R, Weir, M.D., Thomas, G.B, (2014). University Calculus: Early transcendentals, Pearson.
Compendia.