Linear Algebra, 6 credits

Linjär algebra, 6 hp

TNIU75

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

George Baravdish

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 52 h
Recommended self-study hours: 108 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6KFTL Air Transportation and Logistics, Bachelor's Programme 3 (Autumn 2017) 1 1 Swedish Norrköping, Norrköping C
6KLOG Civic Logistics, Bachelor´s Programme 3 (Autumn 2017) 1 1 Swedish Norrköping, Norrköping C
6IBYG Civil Engineering, B Sc in Engineering 3 (Autumn 2017) 1 1 Swedish Norrköping, Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Civil Engineering, B Sc in Engineering
  • Air Transportation and Logistics, Bachelor's Programme
  • Civic Logistics, Bachelor´s Programme

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

After completing this course students should be able to:

  • solve systems of linear equations and be able to interpret these solutions geometrically,
  • handle basic geometric objects in two and three dimensions (like points, vectors, lines, planes) and be able to investigate essential relations between these objects,
  • understand the notion of a matrix and master the matrix calculus in order to perform simple matrix operations (like transposition or multiplication of matrices),
  • understand and apply the notion of basis in space and perform the change of basis,
  • give an account for and perform calculations with the help of basic ideas and methods of theory of linear operators including inverse operators, eigenvalues and eigenvectors, diagonalization of operators (spectral theorem) and dimension theorem as well as relate these to the methods and notions from p. 2, 3, and 4.

Course content

Systems of linear equations. Vectors. Matrices. Determinants. Bases. Change of Bases. The scalar product. The cross product. Lines and planes in space. Linear transformations and their compositions. Eigenvalues and eigenvectors of a linear transformation. Diagonalization. Spectral theorem. Kernel and image of a linear operator. Dimension theorem.

Teaching and working methods

The course consists of lectures and tutorials.

Examination

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

Grades

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

Department

Institutionen för teknik och naturvetenskap

Director of Studies or equivalent

George Baravdish

Examiner

George Baravdish

Course website and other links

http://www2.itn.liu.se/utbildning/kurs/

Education components

Preliminary scheduled hours: 52 h
Recommended self-study hours: 108 h

Course literature

Additional literature

Books

  • Albertson, F, Lineär algebra med vektorgeometri, Övningsbok
    ISBN: 9789144005287
  • Tengstrand, A, Lineär algebra med vektorgeometri
    ISBN: 9789144044187
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. 

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

Additional literature

Books

Albertson, F, Lineär algebra med vektorgeometri, Övningsbok

ISBN: 9789144005287

Tengstrand, A, Lineär algebra med vektorgeometri

ISBN: 9789144044187

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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                            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)
                            
                                
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                            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
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            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
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
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                            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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