Matrices and VectorsLaajuus (3 ECTS)

Objective

After completing the course the student will know the basic concepts related to vectors and matrices with some of their important applications. The student will understand what a digital image is in terms of mathematics.
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After completing the course the student will be able to solve simple mathematical problems by making use of vectors and matrices. The student will be able to construct and solve simple linear models, and interpret their results. The student will be able to do simple image processing in spatial domain.

Content

1. Vector quantities and vectors in a co-ordinate system
2. Matrices and their mappings
3. Solving sets of linear equations by Gaussian elimination and
back-substitution
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4. Applications of vectors and matrices.

Qualifications

Expressions and equations

Assessment criteria, satisfactory (1)

The student knows the basic concepts of vector and matrix. The student is able to do simple calculations with vectors and matrices. The student knows how to model a set of simultaneous linear equations (linear system) by using vector and matrix formalism and how to change from one formalism to another. The student is able to solve linear systems by means of Gaussian elimination and back-substitution in an augmented matrix form.

Assessment criteria, good (3)

In addition to having satisfactory knowledge in the topics of the course the student is able to use vectors and matrices to model and solve simple practical problems. The student knows some sources to define a linear system. The student is able to use a computer system with MATLAB to solve problems with vectors and matrices. The student knows how a digital image can be represented by using matrices.

Assessment criteria, excellent (5)

In addition to having good knowledge in the topics of the course the student is able to apply fluently different standard methods of vectors and matrices to solve engineering problems also with MATLAB. The student is able to use the scalar product of vectors in applications.