Funktiot ja kompleksiluvutLaajuus (3 op)

Osaamistavoitteet

After completing the course the student will know the basic concepts related to functions and complex numbers and some of their important applications. The student will know properties of elementary functions. Will understand ideas related to interpolation.
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After completing the course the student will be able to solve simple mathematical models and interpret their results. The student will be able to apply mapping functions and methods of interpolation in image processing.

Sisältö

1. The concept of the function; the functional relationship
2. Functions and their properties
3. Graphs of functions
4. Interpolation: e.g. nearest neighbour and bilinear interpolation in image processing
5. Complex numbers; their representations and use in applications
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6. Mapping functions in image processing
7. Bayer filter pattern

Esitietovaatimukset

Basics in expressions and equations

Arviointikriteerit, tyydyttävä (1)

The student is able to recognize elementary functions from their graphical representations. The student is able to use functions to solve simple mathematical problems. The student knows how to convert a complex number from one representation to other representations of a complex number. The student can manipulate expressions and solve simple equations with complex numbers.

Arviointikriteerit, hyvä (3)

In addition to having satisfactory knowledge in the topics of the course the student is able to identify a functional relationship between quantities. The student knows how to apply properties of functions to model and solve simple problems in optimization.

Arviointikriteerit, kiitettävä (5)

In addition to having good knowledge in the topics of the course the student is able to apply fluently different standard methods of analysis to solve engineering problems. The student is able to identify when the exponential function can be used to model a problem.