FunctionsLaajuus (3 ECTS)

Objective

The student will understand the basic concepts related to functions. The student will be familiar with the most common functions and able to plot their graphs both by hand and by using some mathematical software. The student will be trained to form graphs for functions, calculate functions etc. for some simple technical applications. The student will be able to solve equations both algebraically and numerically. The student will be able to calculate both the absolute and the relative error of the result. The student will understand the difference between scalar and vector quantities and e.g. add vectors together. The student will learn to use some mathematical software to solve mathematical problems.

Content

Main concepts of functions. Polynomial functions of first, second and third degree. Power-law, exponential and logarithmic functions. Rules of logarithms. Logarithmic scale. Trigonometric functions. Building services engineering applications connected to the aforementioned functions. Calculating absolute and relative errors. The concepts of continuous function and numeric solving of equations. Solving linear and non-linear systems of equations. Scalar and vector quantities, vectors in co-ordinate systems, vector calculations.

Assessment criteria, satisfactory (1)

The student knows the meaning of zero in functions and is able to calculate them. The student is able to calculate the values of functions and recognizes the graphs of the most common functions. The student knows the basic definition of sine and cosine as well as the concept of logarithm. The student is able to solve a simple exponential equation. The student is able to read the logarithmic scale and knows why it is used. The student knows the meaning of direct and inverse proportionality and is able to calculate simple related applications. The student is able to employ simple rules of differentiation and is familiar with derivative as the slope of a tangent and the rate of change of a function. The student is able to use Excel or other computer software to draw graphs of functions.

Assessment criteria, good (3)

In addition to the requirements above, the student is able to employ the rules of logarithms and is able to solve slightly more demanding exponential and logarithmic equations, as well as elementary trigonometric equations. The student is able to use some of the simple transformations of the most common functions and recognizes theirs graphs. The student is familiar with the rules of differentiation and is able to use them well. The student is able to apply functions in examining simple phenomena. The student is able to solve equations numerically.

Assessment criteria, excellent (5)

In addition to the requirements above, the student is able to apply the knowledge and skills acquired during this course and the course Algebra and Geometry to study various phenomena. The student is able to independently choose an appropriate method for solving an equation in each situation.