Functions and Introduction to DifferentiationLaajuus (3 ECTS)

Objective

The student will master some features of basic functions, such as domain, range and zero. The student will be familiar with the graphs of the most common functions as well as with their basic transformations. The student will be able to plot graphs of functions using some mathematical software. 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 use the derivative to determine the rate of change of a function or the optimal values of a function. The student will be able to evaluate derivatives numerically. The student will understand the concepts of functions of several variables and partial derivatives. The student will learn to use some mathematical software to solve mathematical problems.

Content

Main features of the most common functions, graphs and their basic transformations. Most importantly, various sine functions. Rules of logarithms. Logarithmic scale. Functions in physics and in 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. Techniques of differentiation. Graphical and numerical differentiation. Derivative when examining the increase and decrease of a function and determining the optional values. Function of several variables and partial derivative.