| TNA002 |
Linear Algebra, 6 ECTS credits.
/Linjär algebra/
For:
ED
KTS
MT
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Prel. scheduled
hours: 87
Rec. self-study hours: 73
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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 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
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Foundadtion course in mathematics
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 is given in the form of lectures and tutorials.
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Course contents:
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
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Course literature:
Compendium
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Examination: |
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Written examination
Optional written test
Individual assignmnet
Optional written test
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6 ECTS
0 ECTS
0 ECTS
0 ECTS
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Course language is Swedish.
Department offering the course: ITN.
Director of Studies: George Baravdish
Examiner: George Baravdish
Link to the course homepage at the department
Course Syllabus in Swedish
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