# Mathematics II FB2412

## 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:*

- Mathematics that will enable him/her to study the various main courses in the Bachelor’s degree programme, and also provide further specialization in mathematics
- Definitions and concepts related to the course
- The uses, strengths and limitations of various mathematical methods that the course focuses on

*Skills*

*The candidate: *

- Has mastered the use of various mathematical concepts, definitions, formulas and symbols
- Can utilize the mathematical methods that the course focuses on in order to formulate and solve engineering problems
- Can solve mathematical problems using analytical and numerical methods and interpret the results

*General competence*

*The candidate has developed:*

- A precise mathematical language that facilitates communication with others about mathematical problems
- An awareness of the importance of mathematical formalism in solving problems using mathematical models and computational tools

## Course Description

Complex numbers: Basic calculation using complex numbers (Cartesian, polar and exponential forms). Solution of equations with complex solutions.

Linear algebra: Matrix algebra, vector spaces, systems of equations, Gaussian and Gauss-Jordan elimination, eigenvalues and eigenvectors, difference and differential equations and systems thereof.

The Laplace transformation: Transformation theorems, convolution, transformation of periodic functions.

Fourier series: Orthogonal functions, periodic functions, Fourier sinus series and Fourier cosine series.

Taylor series: Series development, Maclaurin series, convergence and approximations.

## Teaching and Learning Methods

Lectures and exercises (exercises are suitable for 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 theory and applications will be illustrated by using realistic examples. Calculation tools will be used in parts of the teaching, preferably in the visualization and analysis of solutions.

The exercises require that students are active (skills). Under supervision, working with exercises can lead to deeper understanding (knowledge) of the interaction between theory, applications and interdisciplinary contexts. The exercises will be done in groups, which will promote the students’ communicative skills in relation to mathematics (general competence).

## Assessment Methods

Individual written mid-term examination that counts for 30% of the final grade.

Individual written examination that counts for 70% of the final grade. Students must achieve a passing mark in the final examination in order to be awarded a passing grade in the course.

*Motivation** *Individual examinations will assess to which extent the individual student has achieved the learning outcomes of the course in terms of knowledge and skills. In addition, the examinations will assess the extent to which the student is able to communicate mathematically through a written paper. The mid-term examination will assess to what degree the learning outcomes have been achieved by the individual student midway through the semester. This motivates students to work in a structured manner throughout the semester.

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

Publisert av / forfatter Marius Lysaker <marius.lysakerSPAMFILTER@hit.no>, last modified Unni Stamland Kaasin - 23/01/2013