Syllabus academic year 2010/2011
(Created 2010-07-25.)
 LINEAR ALGEBRA FMA420
Credits: 6. Grading scale: TH. Cycle: G1 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. FMA420 overlaps following cours/es: FMA012, FMA421 and FMA656. Compulsory for: B1, BI1, C2, D1, E1, F1, I1, K1, L1, N1, Pi1, V1, W2. Course coordinator: Director of Studies Anders Holst, Anders.Holst@math.lth.se, Mathematics. Assessment: Written test comprising theory and problem solving. 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 in mathematics as well as other subjects. The aim is furthermore to develop the student's ability to solve problems and to assimilate mathematical text.

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 its couplings to the concept of a linear transformation, and be able to carrry out elementary matrix operations and to solve matrix equations.

be able to give an overview of and illustrate mathematical concepts in linear algebra that are used to construct and study matematical models in the applications.

be able to explain the contents of some central definitions, theorems and proofs.

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 to independently 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. Rank. Linear transformations. Determinants. Eigenvalues and eigenvectors.

Literature
Sparr, G: Linjär algebra. Studentlitteratur 1994. ISBN 91-44-19752-7