| TAIU05 |
Linear Algebra, 6 ECTS credits.
/Linjär algebra/
For:
DI
EL
KA
Kem
MI
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Prel. scheduled
hours: 56
Rec. self-study hours: 104
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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:
The aim of this course is to acquaint the students with mathematical concepts and methods from linear algebra that are foundational in the natural sciences. Moreover, they should develop an ability to follow and conduct logical reasoning and gain computational and problem solving skills that are essential to further studies in technology and science. After passing the course, one should also be able to understand linear algebraic concepts that frequently occur in technical reports. In order to achieve this, it is necessary to be able to
- solve linear systems of equations using elimination, and to know that such systems have either zero, one or infinitely many solutions.
- carry out matrix computations and solve simple matrix equations.
- define and use the concepts of bases, ON bases and coordinates.
- compute and apply equations for lines and planes.
- compute intersections between lines, between planes and between lines and planes.
- compute distances from points to lines and from points to planes.
- define scalar products and compute scalar products in ON bases.
- use the projection formula.
- define cross products and triple products and compute these in ON bases.
- use the method of least squares.
- compute 2x2 and 3x3 determinants.
- explain the connection between determinants and invertibility of matrices and use determinants for area and volume computations.
- define the concept of linear transformations and find and carry out computations with the corresponding matrices.
- define and compute eigenvalues and eigenvectors of matrices and linear transformations and interpret these notions geometrically.
- use the coordinate identity for basis change and transforming matrices between different bases.
- diagonalise matrices and use this in certain applications.
- solve certain systems of differential equations using diagonalisation methods.
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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:
Lectures and tutorials.
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Course contents:
Systems of linear equations. Matrices and inverses. Geometrical vectors. Scalar product. Vector product and orientation. Determinants. Lines and planes. Method of least squares. Change of basis. Linear mappings and their matrices. Eigenvalues and eigenvectors. The spectral theorem. Systems of differential equations.
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Course literature:
Lemurell, S.: Linjär algebra - från en geometrisk utgångspunkt. Studentlitteratur.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Magnus Herberthson
Link to the course homepage at the department
Course Syllabus in Swedish
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