| TATA67 |
Linear Algebra with geometry, 6 ECTS credits.
/Linjär algebra med geometri/
For:
DPU
EM
M
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Prel. scheduled
hours: 90
Rec. self-study hours: 70
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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:
To give the basic knowledge of linear algebra that is needed in other courses. After the course the student should be able to:
- use coordinates, bases, scalar products, and vector products.
- work with lines, planes and calculate distances.
- solve systems of linear equations.
- use vectors in R^n and matrices.
- use the least squares method.
- compute determinants and use determinants to investigate existence and uniqueness of solutions to quadratic systems of linear equations and existence of inverse of a matrix.
- determine the matrix of a linear transformation.
- use change of basis in order to solve problems.
- compute eigenvalues and eigenvectors, and describe eigenvalues and eigenvectors of a geometrical linear transformation.
- cite the spectral theorem.
- use diagonalisation to solve problems including systems of differential equations, recursive sequences, quadratic forms or powers of matrices.
- perform calculations and verify that the results are correct.
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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:
Teaching is done through lectures and problem classes.
The course runs over the entire autumn semester.
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Course contents:
Linear systems of equations. Geometrical vectors, straight lines and planes. Matrices. Linear spaces. Euclidean spaces. Determinants. Linear mappings. Eigenvalues and eigenvectors. Symmetric mappings. Quadratic forms. Systems of differential equations.
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Course literature:
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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: MAI.
Director of Studies: Jesper Thorén
Examiner: Jan Åslund
Link to the course homepage at the department
Course Syllabus in Swedish
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