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
No published teaching
x

Exam (6 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish

Teaching