Linear Algebra with Geometry, 6 credits

Linjär algebra med geometri, 6 hp

TATA67

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Jan Åslund

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 90 h
Recommended self-study hours: 70 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CDPU Design and Product Development, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping C
6CEMM Energy - Environment - Management, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping C
6CMMM Mechanical Engineering, M Sc in Engineering 1 (Autumn 2017) 1, 2 3, 4 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Design and Product Development, M Sc in Engineering
  • Energy - Environment - Management, M Sc in Engineering
  • Mechanical Engineering, 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

Lycée mathematics and physics (natural sciences or technical programmes).

Intended learning outcomes

To give the basic knowledge of linear algebra that is needed in other courses. After the course the student should be able to:

  • use coordinates, bases, scalar products, and vector products.
  • work with lines, planes and calculate distances.
  • solve systems of linear equations.
  • use vectors in R^n and matrices.
  • use the least squares method.
  • compute determinants and use determinants to investigate existence and uniqueness of solutions to quadratic systems of linear equations and existence of inverse of a matrix.
  • determine the matrix of a linear transformation.
  • use change of basis in order to solve problems.
  • compute eigenvalues and eigenvectors, and describe eigenvalues and eigenvectors of a geometrical linear transformation.
  • cite the spectral theorem.
  • use diagonalisation to solve problems including systems of differential equations, recursive sequences, quadratic forms or powers of matrices.
  • perform calculations and verify that the results are correct.

Course content

Linear systems of equations. Geometrical vectors, straight lines and planes. Matrices. Linear spaces. Euclidean spaces. Determinants. Linear mappings. Eigenvalues and eigenvectors. Symmetric mappings. Quadratic forms. Systems of differential equations.

Teaching and working methods

Teaching is done through lectures and problem classes.
The course runs over the entire autumn semester.

Examination

KTR1Optional written test0 creditsU, G
TEN1Written examination6 creditsU, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Jan Åslund

Course website and other links

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

Education components

Preliminary scheduled hours: 90 h
Recommended self-study hours: 70 h

Course literature

Linjär algebra med geometri, andra upplagan av L Andersson m fl
Code Name Scope Grading scale
KTR1 Optional written test 0 credits U, G
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. 

Linjär algebra med geometri, andra upplagan av L Andersson m fl

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

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
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
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X
TEN1

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
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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