| TATA31 |
Linear Algebra, 8 ECTS credits.
/Linjär algebra/
For:
I
Ii
|
| |
Prel. scheduled
hours: 110
Rec. self-study hours: 103
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G1
|
|
Aim:
To give the basic mathematical knowledge about vectors and matrices which is required for future studies in analysis, numerical analysis, mathematical statistics, economics, cryptography, control theory, optimization, etc. After this course students will be able to handle the linear algebra which is used in other courses in the programme. To pass this course students will need to
- solve systems of linear equations and understand the structure of the solutions
- work with scalar and vector products of geometric vectors
- carry out calculations with matrises and determinants
- understand the concept of vector space, and calculate with vectors and coordinates
- understand the concept of linear transformations, find its matrix and calculate kernel and range
- determine and work with orthonormal bases in Euclidean spaces, apply the 'least-squares' method and use these to calculate the orthogonal projection on a subspace
- determine eigenvectors and eigenvalues, and interpret them geometrically
- understand and apply the principle axes theorem
- understand and use quadratic forms in geometric applications
- work through simple applications to linear differential equations and difference equations
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Foundation course in Mathematics or equivalent
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.
|
|
Organisation:
Teaching is done through lectures and problem classes.
The course runs over the entire autumn semester.
|
|
Course contents:
Systems of linear equations. Geometric vectors, straight lines and planes in three dimensions. Scalar and vector products. Matrices and determinants. General vector spaces and Euclidean spaces. Linear transformations. Eigenvalues and eigenvectors, diagonalisation of matrices, linear transformations, quadratic forms. Conic curves and quadratic surfaces. Elementary applications to linear differential equations and difference equations
|
|
Course literature:
Janfalk, U: Linjär algebra
|
|
Examination: |
|
Written examination
Written test after first half of course.
|
8 ECTS
0 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Ulf Janfalk
Link to the course homepage at the department
Course Syllabus in Swedish
|