Linear Algebra, 6 credits

Linjär algebra, 6 hp

TNA002

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: 87 h
Recommended self-study hours: 73 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping, Norrköping C
6CIEN Electronics Design Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping, Norrköping C
6CMEN Media Technology and Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping, Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Electronics Design Engineering, M Sc in Engineering
  • Communications, Transport and Infrastructure, M Sc in Engineering
  • Media Technology and 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

Foundadtion course in mathematics

Intended learning outcomes

To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, computer graphics, numerical analysis, mathematical statistics, control theory, linear optimization and other subjects. It is also included to develop the ability of using the mathematical language both written and oral. It is necessary for the participant to be able to

  • solve systems of linear equations
  • work with inner and cross product
  • calculate with matrices and determinants
  • calculate with vectors and coordinates in a vector space
  • determine the matrix for a linear transformation and the kernel and the range for such matrices
  • determine ON-basis in an inner product space
  • do orthogonal projection on subspaces and to use least squares approximations
  • solve problems by changing basis
  • determine and to use eigenvalues and eigenvectors in different problems
  • use the spectral theorem in different problems
  • determine the canonical basis of quadratic forms and to use these to solve geometrical problems.
  • carry out inspections of results and partial results, in order to verify that these are correct or reasonable
  • solve system of linear ordinary differential equations

    Course content

    Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces.
    Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Distance and approximation. System of linear ordinary differential equations

    Teaching and working methods

    The course is given in the form of lectures and tutorials.

    Examination

    KTR2Individual assignments0 creditsD
    UPG2Individual assignment0 creditsU, G
    KTR1Individual assignments0 creditsD
    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: 87 h
    Recommended self-study hours: 73 h

    Course literature

    Additional literature

    Compendia


    • Kompendium utgivet vid ITN.
    • Code Name Scope Grading scale
    KTR2 Individual assignments 0 credits D
    UPG2 Individual assignment 0 credits U, G
    KTR1 Individual assignments 0 credits D
    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

    Compendia

    Kompendium utgivet vid ITN.

    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)
    X
    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
    
                                		
                            
                                
    X
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.3 System thinking
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.4 Attitudes, thought, and learning
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                                
     
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.5 Ethics, equity, and other responsibilities
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                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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