Functions and vectorsLaajuus (3 ECTS)

Objective

The student will be familiar with the main elementary functions and is able to use them in applications. The student will recognize scalar and vector quantities and will be familiar with basic vector operations.

Content

The main elementary functions and graphs of them. Scalars and vectors. Vector operations.

Assessment criteria, satisfactory (1)

The student
- knows the meaning of the value of a function in a certain point as well as the meaning of zero point of a function
- is able to form a graph of a simple function with the expression given
- knows what the graph of a linear polynomial function is like and how it changes as the values of parameters a and b change
- knows what the graph of a quadratic polynomial function is like and how it changes as the value of coefficient a changes
- knows the meaning of direct and inverse proportionality
- knows the definition of a logarithm
- is familiar with the basic properties of trigonometric functions and knows how unit circle definition leads to the periodicity of trigonometric functions
- is able to employ simple trigonometric formula and to use vectors in describing directional quantities

Assessment criteria, good (3)

In addition to the requirements above, the student
- is able to employ functions and equations in describing simple phenomena
- is able to solve trigonometric functions, logarithms and other equations with common functions
- is able to solve problems with vector quantities

Assessment criteria, excellent (5)

In addition to the requirements above, the student
- is able to employ functions and equations diversely in describing various types of phenomena
- is able to solve application problems which require synthesizing the knowledge acquired during the course