Engineering mathematics 1Laajuus (5 cr)

Objective

You are able to solve different types of equations and also solve for a variable in a formula.

You know the basic methods for solving a system of equations and are able to use these methods flexibly.

You are familiar with the directional angle and the basic properties of trigonometric functions. You can solve a triangle and understand the prerequisites in the solving process.

You know basic methods for solving a system of equations and are able to use them flexibly.

You know the fundamental properties of vectors and are able to deal with basic vector problems.

You know the idea of the logarithms and are familiar with basic logarithm formulas. You can solve exponential equations and deal with problems of exponential growth and decrease.

Content

How do you solve equations of the first and second degree and square-root equations?

How do you deal with problems of electric circuits, mixture and proportions and curve fitting by forming a system of equations?

How do you solve a triangle? How do you construct basic trigonometric formulas using the unit circle?

How do you solve problems of relative velocity using vectors? How do you use the component form of vector and scalar product for calculating angles and projections?

How do you apply logarithm operations for defining noise levels?

How do you deal with problems of temperature of a cooling particle, decreasing rate of radioactive decay, charging or discharging a capacitor and intensity of radiation e.g. visible light?

Qualifications

General knowledge of mathematics of the upper secondary school or the course of Intensive course in mathematics is required.

Accomplishment methods

Students are able to
use professional vocabulary systematically:
• They know basic concepts and formulas of equations, systems of equations, triangles, unit circle, vectors, logarithms and exponential functions.
• They are able to carry out basic calculations and analyses as well as draw graphs of functions.

identify interrelated tasks:
• They are able to analyse mathematical tasks and solve e.g. problems related to exponential growth.
• They can see methods of application for basic mathematical tools, e.g. vectors.

use the key models, methods, and techniques of the professional field:
• They are able to model and solve small practical problems in mathematics, e.g. solve verbal problems by forming a system of equations.