Study Guide

Objective

You have a good understanding about integral calculus in one variable and skills to apply the basic integration methods.

You are familiar with differential equations of first and second degree and you are able to solve them analytically and numerically.

You know the basic properties of functions of several variables. You are familiar with basic differential calculus of multivariable functions.

Content

How do you carry out more demanding integration tasks by using different integration methods?
How do you perform the change of variable and integration limits when applying the substitution method to definite integral?
What is a partial fraction decomposition of a rational function?
What are differential equations and where are they utilised?
How do you form a differential equation which describes a certain technical phenomenon?
What is a separable differential equation?
How do you solve first and second order linear differential equations with constant coefficients?
How do you solve a differential equation numerically?
How do you illustrate the function of two variables by using equality curves? What are equality surfaces?
What are partial derivatives and how do you find the critical points of a function?
What is the gradient of a function?

Opiskelumateriaali

Lecture notes and calculations.

Yksilölliset oppimisväylät

Final exam.

TKI ja työelämäyhteistyö

This course does not include RDI and work-related cooperation.

Evaluation scale

1-5

Qualifications

The courses ”Engineering mathematics 1, 2 and 3” or comprehensive knowledge of their contents is required.