TAIU05 Linear Algebra 2007

Study Guide@lith

Valid for year : 2007

TAIU05	Linear Algebra, 6 ECTS credits. /Linjär algebra/ For: DI EI KA MI OI
	Prel. scheduled hours: 56 Rec. self-study hours: 104
	Area of Education: Science Subject area: Mathematics
	Advancement level (G1, G2, A): G1
	Aim: After completing this course, students should be acquainted with those mathematical concepts and methods from the theory of linear algebra that are fundamental for the study of science and technology. Furthermore, they shall posess the ability to follow and independently pursue mathematical and logical arguments, as well as the ability to calculate and solve problems occuring in their further studies in technology and science. Anyone having passed the course should be able to read and understand the linear algebra that occurs frequently in articles in technical journals. To this end, it is vital that the students Can solve systems of linear equations. Know that such systems may lack solutions, or posess infinitely many solutions Understand the concept of basis and coordinates Know the equations of lines and planes, and how intersections between those can be calculated Know about scalar products and vector products Know the definition of 2x2 and 3x3 determinants, and their relations to the solution of linear systems of equations, as well as the geometrical interpretation as a volume. Be familiar with the change-of-basis formulae Know the definition of eigenvectors and eigenvalues, how they can be calculated, and how they can be used to diagonalize linear maps. Can apply this knowledge to the solution of certain systems of ODE's.
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Lycée mathematics (natural sciences or technical programmes). Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
	Organisation: Lectures and tutorials.
	Course contents: Systems of linear equations. Matrices and inverses. Geometrical vectors. Scalar product. Vector product and orientation. Determinants. Lines and planes. Method of least squares. Change of basis. Linear mappings and their matrices. Eigenvalues and eigenvectors. The spectral theorem. Systems of differential equations.
	Course literature: Tengstrand, A: Lineär algebra med vektorgeometri. Studentlitteratur. Material produced at the Department och Mathematics
	Examination:
	Written examination	4 p	/	6 ECTS


Course language is Swedish. Department offering the course: MAI. Director of Studies: Göran Forsling Examiner: Jan Snellman Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 11/05/2006