Linear Algebra, 8 credits
Linjär algebra, 8 hp
TATA24
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Göran Bergqvist (FyN,Mat,Y,Yi, MED) och Tomas Sjödin (D,U,IT)Director of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 108 hRecommended self-study hours: 105 h
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 MathematicsCourse level
First cycleAdvancement level
G1XCourse 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
KTR1 | Written test | 0 credits | U, G |
TEN1 | Written examination | 8 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Linear Algebra, honours course, Functional Analysis, Numerical Linear Algebra
Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
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.htmlEducation components
Preliminary scheduled hours: 108 hRecommended 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.
Additional literature
Books
Compendia
Other
Note: The course matrix might contain more information in Swedish.
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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) |
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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) |
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1.5 Insight into current research and development work |
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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 |
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2.4 Attitudes, thought, and learning |
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2.5 Ethics, equity, and other responsibilities |
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3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
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3.2 Communications |
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3.3 Communication in foreign languages |
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4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
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4.3 Conceiving, system engineering and management |
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4.5 Implementing |
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4.6 Operating |
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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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5.5 Presentation and evaluation of research or development projects |
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