MATA2710 Linear algebra and differentiation for engineering (6 cr)
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028
Tweet text
Opintojakso on tarkoitettu ensisijaisesti tekniikan alan kandidaatti- ja DI-ohjelmien opiskelijoille ja ohjelmiin hakemista suunnitteleville.
Description
- Linear transformation, and linear and affine functions in one and two dimensions.
- Systems of linear equations and their representation as matrix equations (underdetermined and overdetermined systems).
- Identity matrix, inverse matrix, determinant, singularity, and submatrices.
- Symmetric matrix, transpose, and trace.
- Composition of linear transformations and matrix products.
- Change of basis.
- Eigenvalues and eigenvectors.
- Inner product.
- General finite-dimensional vector space.
- Definition of the derivative of a function.
- Directional derivative, gradient, and potential function.
- Jacobian matrix.
- Application of linear algebra and derivatives in image processing using Python and the OpenCV library.
Learning outcomes
After completing the course, the student:
- Can identify linear, affine, and non-linear functions.
- Is familiar with the basic concepts of matrix algebra.
- Can represent a system of linear equations, its solution, and the composition of linear transformations in matrix form, and masters the calculation of matrix products.
- Understands the effect of a basis change on the matrix representing a linear transformation.
- Can derive a scalar function and recognizes the derivative as a linear transformation.
- Has been introduced to the use of basic concepts of linear algebra and differentiation in image processing.
Additional information
Molempia opintojaksoja MATP121 Lineaarinen algebra ja geometria 1 sekä MATA2710 Lineaarialgebra ja derivointi tekniikan alalla ei voi sisällyttää matematiikan opintokokonaisuuteen.
Description of prerequisites
MATP1700 Introductory
Course to Mathematics in Engineering
Completion methods
Method 1
Evaluation criteria:
Harjoitukset ja kurssitentti. Tarkemmat arviointiperusteet ilmoitetaan opetusohjelmassa.
Time of teaching:
Period 4
Select all marked parts
Method 2
Evaluation criteria:
Lopputentin pistemäärä
Select all marked parts
Parts of the completion methods
x
Participation in teaching (6 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
x
Exam (6 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish