(Created 2010-07-25.)
 LINEAR ALGEBRA WITH SCIENTIFIC COMPUTATION FMA421
Credits: 9. Grading scale: TH. Cycle: G1 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. FMA421 overlaps following cours/es: FMA420 and FMA656. Compulsory for: M1, MD1. Course coordinator: Director of Studies, Anders Holst, Anders.Holst@math.lth.se, Mathematics. Assessment: Part 1: Written test comprising theory and problem solving (the same as the examination for FMA420). Part 2: Compulsory computer work. Examination in a computer laboratory. The final grade is decided by the result on the test in part 1. Parts: 2. 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 also to develop the student's ability to solve problems and to assimilate mathematical text.

Furthermore, the course aims at giving basic ability to use of computer software to convert mathematical theory into numerical computations. The students should become familiar with Matlab, its syntax and structures. The course is intended as a basis for other courses which use Matlab.

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.

be able to use Matlab to carry out computations with concepts and objects from linear algebra.

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.

be able to visualise mathematical results in Matlab.

be able to use basic computation methods in Matlab.

Contents
Linear algebra:

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.

Scientific computation:

Introduction to Matlab and its use for computation with vectors and matrices. Basic knowledge about files and editing. Basic Matlab. Graphics. Numerical methods in linear algebra (solving linear systems of equations, computation of eigenvalues, least squares approximation) with applications in mechanics.

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

Parts

Code: 0103. Name: Linear Algebra.
Higher education credits: 6. Grading scale: TH. Assessment: Written test comprising theory and problem solving. Contents: See above, Linear algebra.

Code: 0203. Name: Introduction to Scientific Computation.
Higher education credits: 3. Grading scale: UG. Assessment: Compulsory computer work. Examination in a computer laboratory. Contents: See above, Scientific computing.