FunctionsLaajuus (3 ECTS)

Objective

On completion of the course the student will master some features of basic functions. The student will be familiar with the graphs of the most common functions, as well as with their basic transformations. The student will be familiar with the applications of functions in physics and building services engineering. On completion of the course the student will be able to solve equations both algebraically and numerically. The student will understand the concept of derivative and master the basic techniques of differentiation. The student will be able to draw graphs of functions and use Excel or other computer software to solve equations numerically.

Content

The main features of polynomial, power, exponential and logarithmic functions, their graphs and basic transformations. Inverse and direct proportionality. The concept and rules of logarithm, logarithmic scale. Solving exponential and logarithmic equations. Functions in physics and building services engineering. Algebraic and numeric solving of equations. The concepts of continuity and derivative. Derivative as the slope of a tangent and the rate of change of a function. Rules of differentiation. Function of several variables and partial derivative.

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 the graphs of them. 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.