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Linear Algebra, 8 credits

Linjär algebra, 8 hp

TATA31

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Ulf Janfalk

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 110 h
Recommended self-study hours: 103 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CIEI	Industrial Engineering and Management - International, M Sc in Engineering - Chinese	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C
6CIEI	Industrial Engineering and Management - International, M Sc in Engineering - French	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C
6CIEI	Industrial Engineering and Management - International, M Sc in Engineering - German	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C
6CIEI	Industrial Engineering and Management - International, M Sc in Engineering - Japanese	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C
6CIEI	Industrial Engineering and Management - International, M Sc in Engineering - Spanish	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C
6CIII	Industrial Engineering and Management, M Sc in Engineering	1 (Autumn 2017)	1, 2	2, 2	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Industrial Engineering and Management - International, M Sc in Engineering
Industrial Engineering and Management, M 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.

Prerequisites

Foundation course in Mathematics or equivalent

Intended learning outcomes

To give the basic mathematical knowledge about vectors and matrices which is required for future studies in analysis, numerical analysis, mathematical statistics, economics, cryptography, control theory, optimization, etc. After this course students will be able to handle the linear algebra which is used in other courses in the programme. To pass this course students will need to

solve systems of linear equations and understand the structure of the solutions
work with scalar and vector products of geometric vectors
carry out calculations with matrises and determinants
understand the concept of vector space, and calculate with vectors and coordinates
understand the concept of linear transformations, find its matrix and calculate kernel and range
determine and work with orthonormal bases in Euclidean spaces, apply the 'least-squares' method and use these to calculate the orthogonal projection on a subspace
determine eigenvectors and eigenvalues, and interpret them geometrically
understand and apply the principle axes theorem
understand and use quadratic forms in geometric applications
work through simple applications to linear differential equations and difference equations

Course content

Systems of linear equations. Geometric vectors, straight lines and planes in three dimensions. Scalar and vector products. Matrices and determinants. General vector spaces and Euclidean spaces. Linear transformations. Eigenvalues and eigenvectors, diagonalisation of matrices, linear transformations, quadratic forms. Conic curves and quadratic surfaces. Elementary applications to linear differential equations and difference equations

Teaching and working methods

Teaching is done through lectures and problem classes.

Examination

KTR1	Written test	0 credits	U, G
TEN1	Written examination	8 credits	U, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Ulf Janfalk

Education components

Preliminary scheduled hours: 110 h
Recommended self-study hours: 103 h

Course literature

Janfalk, U: Linjär algebra

Code	Name	Scope	Grading scale
KTR1	Written test	0 credits	U, G
TEN1	Written examination	8 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.

Janfalk, U: Linjär algebra

Download

Download course literature list as PDF

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

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)		X	X	KTR1 TEN1
	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)	X
	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	TEN1
	2.2 Experimentation, investigation, and knowledge discovery		X	X
	2.3 System thinking
	2.4 Attitudes, thought, and learning		X	X	KTR1 TEN1
	2.5 Ethics, equity, and other responsibilities		X
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork			X
	3.2 Communications	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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