Learning outcome

After successfully completing the course, the candidate will have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Knowledge

The candidate:

• Has knowledge of the multi-variable functions, vector analysis and partial differential equations that provide a foundation for Master’s degree programmes in engineering.
• Has an understanding of the relationship between the analytical and geometric representations of curves, surfaces, functions and vector fields, and is able to formulate problems mathematically and interpret results adequately
• Has insight into how ordinary methods, Fourier series, Laplace transform and Fourier transform can be used to solve certain types of partial differential equations
• Can, by logical reasoning, clarify how changes in assumptions for models and calculations can affect the final result

Skills

The candidate:

• Can create simple sketches and perform simple manual calculations within the areas the he/she should have knowledge of
• Is able to use the computer program Maple to generate illustrations, animations and perform complex calculations within the areas he/she should have knowledge of

General competence

The candidate:

• Has developed the capability to make precise mathematical formulations that enable good communication with others about relevant problems
• Has developed an awareness of the importance of mathematical formalism to solve problems using mathematical models.

Course Description

Quadratic surfaces. Vector functions. Functions of several variables. Lagrange multiplier. Core rules. Multiple integration. Polar, cylindrical and spherical coordinates. General variable changes. Vector fields. Line integrals. Surface integrals. Green’s, Gauss’s and Stokes’s integrals. Classification of partial differential equations. D’Alembert’s solution. Solution methods of ordinary differential equations. Using Fourier series, Laplace and Fourier transforms. Separation of variables method. Animations and numerical solutions. Physical interpretations.

Teaching and Learning Methods

Lectures, exercises and group work.

Motivation

The lectures will provide an overview of the course’s academic content (knowledge) and encourage students to work independently (skills), for instance, by reviewing examples and by showing what can be achieved by using computers. The lectures will also illustrate a relevant mathematical formulation level, both orally and in writing (general competence).

The exercises require that students themselves are active (skills). Under supervision, working with exercises can lead to deeper understanding (knowledge) of the interaction between instrumental activities and theory. The exercises also promote mathematical communication between students and between the tutor and student (general competence).

Group work is necessary in order to develop students’ communicative abilities in mathematics (general competence). In addition, group work can include assignments that require calculations (skills), creativity and innovation (knowledge).

Assessment Methods

1. Continuous assessment:

Group work using software Maple will be important (weighted 30%). The group work will be assessed with a letter grade.

2. Final assessment:

Individual written examination (weighted 70%).

Students must receive a grade of E or better in the final examination in order to gain a final passing grade for the course.

All written and printed materials may be used in the final examination, as well a computer.

Motivation

The final examination will assess the extent to which the individual student has achieved the learning outcomes in terms of knowledge and skills, but will also implicitly express the candidate’s mathematical formulation ability (general competence). The group work will normally include both the knowledge and skill-related elements, but will also test the extent to which the student is able to communicate mathematically within a group and through a written report.

Minor adjustments may occur during the academic year, subject to the decision of the Dean