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Linear Algebra, 8 ECTS credits.
/Linjär algebra/
For:
D
FyN
IT
Mat
MED
U
Y
Yi
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Prel. scheduled
hours: 108
Rec. self-study hours: 105
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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, 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
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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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Supplementary courses:
Linear Algebra, honours course, Functional Analysis, Numerical Linear Algebra
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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. Vector spaces. Euclidean spaces. Determinants. Linear mappings. Eigenvalues and eigenvectors. Symmetric mappings. Quadratic forms. Systems of differential equations.
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Course literature:
Janfalk, U.: Linjär algebra.
Exempelsamling i linjär algebra.
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Examination: |
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Written examination
Written test
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8 ECTS
0 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Jesper Thorén (FyN,Mat,Y,Yi, MED), Tomas Sjödin (D,IT,U)
Link to the course homepage at the department
Course Syllabus in Swedish
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