IRF30014 Mathematics 3 (Autumn 2015)

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, or equivalent, is recommended.

Lecture Semester

5^th semester (autumn)

The student's learning outcomes after completing the course

Knowledge:

The student 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 learnt calculus in multiple variables
• have basic knowledge of partial differential equatations
• have a good knowledge in thermal physics and can do modelling of heat transfer problems, and show an understanding of the model´s limitation.

Skills:

The student

• has the necessary skills and methodic understanding of matematics and physics for further master studies in technology
• is able to do mathematical reasoning and draw logical conclusions

• can perform calculations related to the course subjects
• can understand and justify their calculations
• can apply mathematics to problems in engineering sciences
• can use mathematical software for simple simulations
• has skills in quantitive methods, and can make models based on mathematical and physical principles and collect, analyze and present numerical data.

Competence:

The student

• understands that the mathematical language has a level of precision appropriate for structuring and solve engineering problems
• has gained an understanding of mathematics 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, Hesse matrix, classification of critical points in dimensions, Lagrange multipliers
• Vector fields, Jacobi matrix
• Multiple integrals in two and three dimensions
• Line and surface integrals
• Green’s, Stokes’ and Divergence theorems
• Partial differential equations, heat conduction equation and the wave equation in one dimension
• Use of mathematical software, numerical methods
• Examples from electrical circuits, static and dynamic systems, which in turn gives multivariable linear equation.
• Electrical and magnetic fields
• Thermical 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