Engineering MathematicsLaajuus (4 op)

Osaamistavoitteet

After completing the course the student will recognise typical mathematical structures and know their basic properties. Will know several ways to represent data and information. Will understand how to represent changes in exact mathematical ways. Understands what a digital image is in terms of mathematics.
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After completing the course the student will be able to manipulate expressions by hand and by a computer. Will be able to analyse functions to get insight in the properties of functions. Will be able to model simple practical problems and solve them. Will be able to process images with histogram methods. Will be able to use a computer to solve simple engineering problems.

Sisältö

Rules of algebra especially in modifying expressions. Solving equations and sets of equations. Elementary functions in engineering applications, graphs of functions. Matrix as an aggregate of data, basics of modelling by matrices and vectors. Mathematics for changes: esp. derivative as a rate of change of a quantity. Dealing with numerical data in applications: esp. interpolation and numerical derivative, curve fitting. Digital image in spatial domain, modifying an image by histogram methods. Basics of computer mathematics.
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Standard matrix of a linear transformation; homogenous co-ordinates. Special forms of numerical derivatives. Least squares method (LSM); interpolation and curve fitting with LSM.

Esitietovaatimukset

Finnish Gymnasium with long studies in Mathematics or equivalent.

Lisätiedot

Contact teaching, laboratory exercises and homework, group work.