Linear Algebra, 8 credits

Linjär algebra, 8 hp

TATA24

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Göran Bergqvist (FyN,Mat,Y,Yi, MED) och Tomas Sjödin (D,U,IT)

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 108 h
Recommended self-study hours: 105 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
Single subject course (One-third-time, Day-time) Autumn 2017 - Swedish Linköping, Valla
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Chinese 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, French 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, German 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Japanese 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Spanish 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CMED Biomedical Engineering, M Sc in Engineering 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6CDDD Computer Science and Engineering, M Sc in Engineering 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping, Valla C
6CMJU Computer Science and Software Engineering, M Sc in Engineering 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping, Valla C
6CITE Information Technology, M Sc in Engineering 3 (Autumn 2017) 1, 2 4, 4 Swedish Linköping, Valla C
6KMAT Mathematics, Bachelor's Programme 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C
6KFYN Physics and Nanoscience, Bachelor's Programme 1 (Autumn 2017) 1, 2 1, 4 Swedish Linköping, Valla C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Biomedical Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Physics and Nanoscience, Bachelor's Programme
  • Mathematics, Bachelor's Programme
  • Computer Science and Software Engineering, M Sc in Engineering
  • Computer Science and Engineering, M Sc in Engineering
  • Information Technology, 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

Admisson to the course requires , as well as general university requirements, secondary school mathematics (or equivalent).

Intended learning outcomes

To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, numerical analysis, mathematical statistics, control theory, linear optimisation and other subjects. After completing the course the students will be able to read and understand the linear algebra which is used in other courses within the programme and the linear algebra which can be found in technical articles. In order to handle this it is necessary to be able to

  • solve systems of linear equations and know of the structure of the set of solutions
  • work with inner product and vector product for geometrical vectors
  • perform calculations with matrices and determinants
  • describe the concept of a vector space and perform calculations with vectors and coordinates
  • describe the concept of a linear mapping, determine the matrix of a linear mapping and calculate the null space and the range
  • project orthogonally on subspaces and use the method of least squares
  • use a change of basis in order to solve problems
  • formulate the spectral theorem and use it in order to solve systems of differential equations and systems of difference equations

 

Course content

Linear systems of equations. Geometrical vectors, straight lines and planes. Matrices. Vector 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

KTR1Written test0 creditsU, G
TEN1Written examination8 creditsU, 3, 4, 5

Grades

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

Other information

Supplementary courses: Linear Algebra, honours course, Functional Analysis, Numerical Linear Algebra

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Göran Bergqvist (FyN,Mat,Y,Yi, MED) och Tomas Sjödin (D,U,IT)

Course website and other links

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

Education components

Preliminary scheduled hours: 108 h
Recommended self-study hours: 105 h

Course literature

Additional literature

Books

  • Janfalk, U, Linjär algebra

Compendia

Other

  • Exempelsamling i 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)

Additional literature

Books

Janfalk, U, Linjär algebra

Compendia

Other

Exempelsamling i linjär algebra

Download

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)
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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
                            
                                
 

                            		
                            
                                
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                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
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                            2.3 System thinking
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.4 Attitudes, thought, and learning
                            
                                
 

                            		
                            
                                
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                            2.5 Ethics, equity, and other responsibilities
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
                    
                        

                            
                                3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
                            
                        

                    
                    
                        

                            
                            3.1 Teamwork
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            3.2 Communications
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
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                            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
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
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                            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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