| TNIU75 |
Linear Algebra, 6 ECTS credits.
/Linjär algebra/
For:
BI
FT
SL
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Prel. scheduled
hours: 52
Rec. self-study hours: 108
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
The course consists of lectures and tutorials.
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Course contents:
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.
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Course literature:
Tengstrand, A: Lineär algebra med vektorgeometri. Studentlitteratur. ISBN: 9789144044187.
Albertson, F: Lineär algebra med vektorgeometri. �-vningsbok. Studentlitteratur. ISBN: 9789144005287.
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Examination: |
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Written examination
Optional written test
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6 ECTS
0 ECTS
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Course language is Swedish.
Department offering the course: ITN.
Director of Studies: George Baravdish
Examiner: Claes Algström
Link to the course homepage at the department
Course Syllabus in Swedish
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