Differentiaali- ja integraalilaskentaLaajuus (3 op)

Osaamistavoitteet

After completing the course the student will recognise typical mathematical structures and know their basic properties. The student will know several ways to represent data and information. The student will understand how to represent changes in an exact mathematical way.
The student will understand the basic concepts in integration. The student will understand the role of differentiation and integration in engineering applications. The student will understand some basic methods in manipulating a digital image.
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After completing the course the student will be able to manipulate expressions by hand and by a computer. The student will be able to analyse functions to get insight into the properties of functions. The student will be able to model simple practical problems in calculus and solve them analytically or numerically. The student will be able to use a computer to solve simple engineering problems. The student will be able to process images by histogram and mask methods in spatial domain by using a computer.

Sisältö

1. Mathematics of changes: absolute change, average change, derivative
2. Definite integral and integral function
3. Differentiation and integration with data
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4. Gradient and directional derivative
5. Related mask-methods

Esitietovaatimukset

Functions and complex numbers

Arviointikriteerit, tyydyttävä (1)

The student knows the concepts of derivative and integral and is able to differentiate and integrate elementary functions. The student can approximate numerically a derivative and a definite integral of a function.

Arviointikriteerit, hyvä (3)

In addition to having satisfactory knowledge in the topics of the course the student is able to apply methods of calculus to model and solve problems in optimization. The student can analyse numerical data by means of calculus.

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 calculus to solve engineering problems. The student knows how a derivative can be used to detect edges in an image.