Linear Algebra, 6 credits

Linjär algebra, 6 hp

TAIU05

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Magnus Herberthson

Director of studies or equivalent

Jesper Thore'n

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6IKEA	Chemical Analysis Engineering, B Sc in Engineering	2 (Spring 2017)	1	4	Swedish	Linköping, Valla	C
6KKEM	Chemistry	6 (Spring 2017)	1	4	Swedish	Linköping, Valla	E
6IDAT	Computer Engineering, B Sc in Engineering	2 (Spring 2017)	1	4	Swedish	Linköping, Valla	C
6IELK	Engineering Electronics, B Sc in Engineering	2 (Spring 2017)	1	4	Swedish	Linköping, Valla	C
6IMAS	Mechanical Engineering, B Sc in Engineering	2 (Spring 2017)	1	4	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Computer Engineering, B Sc in Engineering
Chemistry
Engineering Electronics, B Sc in Engineering
Chemical Analysis Engineering, B Sc in Engineering
Mechanical Engineering, B Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Intended learning outcomes

The aim of this course is to acquaint the students with mathematical concepts and methods from linear algebra that are foundational in the natural sciences. Moreover, they should develop an ability to follow and conduct logical reasoning and gain computational and problem solving skills that are essential to further studies in technology and science. After passing the course, one should also be able to understand linear algebraic concepts that frequently occur in technical reports. In order to achieve this, it is necessary to be able to

solve linear systems of equations using elimination, and to know that such systems have either zero, one or infinitely many solutions.
carry out matrix computations and solve simple matrix equations.
define and use the concepts of bases, ON bases and coordinates.
compute and apply equations for lines and planes.
compute intersections between lines, between planes and between lines and planes.
compute distances from points to lines and from points to planes.
define scalar products and compute scalar products in ON bases.
use the projection formula.
define cross products and triple products and compute these in ON bases.
use the method of least squares.
compute 2x2 and 3x3 determinants.
explain the connection between determinants and invertibility of matrices and use determinants for area and volume computations.
define the concept of linear transformations and find and carry out computations with the corresponding matrices.
define and compute eigenvalues and eigenvectors of matrices and linear transformations and interpret these notions geometrically.
use the coordinate identity for basis change and transforming matrices between different bases.
diagonalise matrices and use this in certain applications.
solve certain systems of differential equations using diagonalisation methods.

Course content

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.

Teaching and working methods

Lectures and tutorials.

Examination

TEN1

Written examination

6 credits

U, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thore'n

Examiner

Magnus Herberthson

Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Code	Name	Scope	Grading scale
TEN1	Written examination	6 credits	U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Course literature is preliminary.

There is no course literature available for this course in studieinfo.

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	X
	1.2 Fundamental engineering knowledge (G1X level)	X
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving		X	X
	2.2 Experimentation, investigation, and knowledge discovery
	2.3 System thinking
	2.4 Attitudes, thought, and learning		X	X
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork
	3.2 Communications		X	X
	3.3 Communication in foreign languages
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context
	4.3 Conceiving, system engineering and management
	4.4 Designing
	4.5 Implementing
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects

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