Course syllabus

# Linjär algebra med introduktion till datorhjälpmedel Linear Algebra with Introduction to Computer Tools

## FMAA20, 7,5 credits, G1 (First Cycle)

Valid for: 2014/15
Decided by: Education Board B
Date of Decision: 2014-04-08

## General Information

Main field: Technology.
Compulsory for: B1, K1
Language of instruction: The course will be given in Swedish

## Aim

The aim of the course is to give a basic introduction to linear algebra. A further aim is to give basic proficiency in Matlab as a basis for later courses.

Particular emphasis is put on the role which linear algebra plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies in mathematics as well as other subjects. The aim is furthermore to develop the students' ability to solve problems and to assimilate mathematical text.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• with confidence be able to solve linear systems of equations and be able to demonstrate an ability to geometrically interpret the solutions of such systems.
• be able to represent, handle and compute with - with and without computer - basic geometrical objects in three dimensions, such as points, vectors, lines and planes.
• be able to show a general knowledge of the matrix concept and of its coupling to the concept of a linear transformation, and be able to carry out elementary matrix operations and to solve matrix equations, with and without computer.
• be able to give an overview of and illustrate mathematical concepts in linear algebra that are used to construct and study mathematical models in applications.
• be able to explain the contents of some central definitions, theorems and proofs.
• be able to account for the method of least squares.

Competences and skills
For a passing grade the student must

• be able to demonstrate a good ability to carry out algebraic calculations within in the framework of the course.
• in connection with problem solving, be able to demonstrate an ability to independently choose and use mathematical methods within linear algebra.
• in connection with problem solving, be able to demonstrate an ability to integrate concepts from the different parts of the course.
• be able to demonstrate an ability to explain mathematical reasoning in a structured and logically clear way.
• be able to graphically  illustrate sets of points in the plane using a computer, and to adapt curves to these.

## Contents

• Systems of linear equations.
• Vectors. Bases and coordinate systems. Equations for lines and planes in space. Scalar product with applications. Vector product with applications.
• Matrices. Rank. Linear transformations. Determinants. Eigenvalues and eigenvectors.
• Matlab as computational and graphical tool.

## Examination details

Assessment: Written exam on Linear algebra. Oral exam with computer on Matlab capability. The final grade is the grade obtained in the written exam.

Parts
Code: 0115. Name: Linear Algebra.
Credits: 6. Grading scale: TH. Assessment: Written exam. Further information: This is the same exam as for FMA420.
Code: 0215. Name: Basic Computer Ability.
Credits: 1,5. Grading scale: UG. Assessment: Oral exam based on the computer sessions during the course.

Required prior knowledge: FMAA01/05 Calculus in one variable.
The number of participants is limited to: No
The course overlaps following course/s: FMA420, FMA421, FMA656