Engineering mathematics 4Laajuus (5 cr)

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?

Qualifications

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

Accomplishment methods

Students can
- use professional vocabulary systematically
- they know basic concepts and formulas of integral calculus, differential equations and functions of several variables
- carry out calculations and analyses
- identify interrelated tasks
- combine mathematical formulas and rules to form more demanding mathematical structures
- see methods of application for mathematical structures
- use the key models and methods of the professional field
- model and solve practical problems mathematically.