IRF30014 Mathematics 3 (Autumn 2016)

The course is connected to the following study programs

The course is an optional course in all bachelor of engineering programmes

Prerequisites

Successful completion of the courses Mathematics 1 and Mathematics 2 and Physics/Chemistry, or equivalent, is recommended.

Lecture Semester

5^th semester (autumn)

The student's learning outcomes after completing the course

Knowledge:

The students will

• have learnt 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 of several variables
• have some knowledge of the partial differential equations related to heat transfer and waves
• have good knowledge of thermal physics an be able to model heat transfer, and understand the limitations of the model

Skills:

The students

• have the mathematical and physical prerequisits for a masters programme in engineering
• are able to ressonate and draw logical conclusions
• are able to perform calculations related to the course subjects
• understand and can justify their calculations
• are able to apply mathematics to problems in engineering sciences
• are able to use mathematical software for simple simulations
• have quantitative problem solving skills and are able to model by using basic principles from mathematics and physics, and are able to collect, analyze and present numerical data

Competence:

The students

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

Content

• Curves in parametric form and in polar coordinates, curvature and torsion
• Quadratic forms, orthogonal diagonalization and quadric surfaces
• Functions of several variables, Hessian, classification of critical points in n dimensions, Lagrange multipliers
• Vector fields, Jacobi matrix
• Multiple integrals in two and three dimensions
• Line and surface integrals
• Green's, Stokes' and the divergence theorems
• Partial differential equations, heat equation and the wave equation in one dimension
• Use of mathematical software, numerical methods
• Examples from electric circuits, static and dynamical systems leading to linear equations in several variables
• Electric and magnetic fields
• Thermic physics, convection, radiation and diffusion

Forms of teaching and learning

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

Coursework requirements - conditions for taking the exam

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 of 4 hours.
An approved calculator and all written aids are permitted at the exam.
The A-F grading system is used, with A as the best mark and F as fail.

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, Weir & Thomas (2012). University Calculus, early transcendentals, 2^nd ed., Pearson
Compendia