Engineering mathematics 4Laajuus (5 cr)
Code: TY00EL02
Credits
5 op
Teaching language
- Finnish
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.
Enrollment
01.01.2024 - 24.12.2024
Timing
01.01.2024 - 31.12.2024
Number of ECTS credits allocated
5 op
Virtual portion
4 op
Mode of delivery
20 % Contact teaching, 80 % Distance learning
Unit
Department of Construction and Energy Engineering
Campus
Ecampus
Teaching languages
- Finnish
Seats
0 - 40
Teachers
- Lassi Salminen
- Henry Lähteenmäki
Teacher in charge
Lassi Salminen
Groups
-
VV2024-2025Optional studies 2024-2025
-
VV2023-2024Optional studies 2023-2024
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
Opiskelu tapahtuu kokonaan verkossa, materiaali on Learn-alustalla.
Evaluation scale
1-5
Qualifications
The courses ”Engineering mathematics 1, 2 and 3” or comprehensive knowledge of their contents is required.
Enrollment
17.04.2023 - 07.05.2023
Timing
09.01.2023 - 31.12.2023
Number of ECTS credits allocated
5 op
Virtual portion
4 op
Mode of delivery
20 % Contact teaching, 80 % Distance learning
Unit
Department of Construction and Energy Engineering
Campus
Ecampus
Teaching languages
- Finnish
Seats
0 - 40
Teachers
- Lassi Salminen
- Henry Lähteenmäki
Teacher in charge
Henry Lähteenmäki
Groups
-
VV2022-2023Optional studies 2022-2023
-
VV2023-2024Optional studies 2023-2024
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.
Enrollment
23.08.2021 - 01.02.2022
Timing
30.08.2021 - 31.07.2022
Number of ECTS credits allocated
5 op
Virtual portion
5 op
Mode of delivery
Distance learning
Unit
Department of Construction and Energy Engineering
Campus
Ecampus
Teaching languages
- Finnish
Seats
0 - 100
Teachers
- Lassi Salminen
- Henry Lähteenmäki
Teacher in charge
Lassi Salminen
Groups
-
VV2021-2022Optional studies 2021-2022
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.