(Created 2008-07-17.)
 MATHEMATICS, LINEAR ALGEBRA FMA656

Higher education credits: 4,5. Grading scale: TH. Level: G1 (First level). Language of instruction: The course will be given in Swedish. FMA656 overlap following cours/es: FMA420, FMA421, FMA420 och FMA421. Compulsory for: IBYA1, IBYI1, IBYV1, IDA1, IDL1. Course coordinator: Director of Studies, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Assessment: Written test. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The course aims at giving a basic treatment of linear algebra. Particular emphasis is on the role this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies.

Knowledge and understanding
For a passing grade the student must

• with confidence be able to solve linear systems of equations and be able to show capability to geometrically interpret such systems.

• be able to represent, handle and compute with basic geometrical objects in three dimensions, such as points, vectors, lines and planes.

• be able to show general knowledge of the matrix concept, and be able to carrry out elementary matrix operations and to solve matrix equations.

Skills and abilities
For a passing grade the student must

• be able to demonstrate good algebraic computation ability.

• in connection with problem solving be able to show capability independently to choose and use mathematical methods within linear algebra.

• in connection with problem solving be able to show capability to integrate concepts from different parts of the course.

• be able to show capability to explain mathematical reasoning in a structured and logically clear way.

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. Linear transformations. Determinants.

Literature
Sparr, G: Linjär algebra. Studentlitteratur. ISBN: 9789144197524.