Differential EquationsLaajuus (3 cr)
Code: TKV22MA05
Credits
3 op
Objective
The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.
Content
- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad
Qualifications
Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.
Assessment criteria, satisfactory (1)
Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.
Assessment criteria, good (3)
Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.
Assessment criteria, excellent (5)
Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.
Materials
Course notes with theory and exercises
Selected parts from:
- Engineering mathematics - A Foundation for electronic, electrical, communications and system engineers, third edition (Croft, Davison, Hargreaves)
- Differentiaaliyhtälöt TAM 3D (Launonen, Sorvali, Toivonen)
Enrollment
01.12.2024 - 09.03.2025
Timing
03.03.2025 - 25.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
Campus
Vasa, Wolffskavägen 33
Teaching languages
- Svenska
Degree programmes
- Degree Programme in Civil and Construction Engineering
- Degree Programme in Mechanical and Production Engineering
- Degree Programme in Electrical Engineering and Automation
- Degree Programme in Industrial Management
Teachers
- Ing-Britt Rögård
Teacher in charge
Leif Östman
Scheduling groups
- BYS22-K (Size: 40. Open UAS: 0.)
- BYS23-P (Size: 40. Open UAS: 0.)
- BYS22-P (Size: 40. Open UAS: 0.)
- BYS23-K (Size: 40. Open UAS: 0.)
Groups
-
BYS23D-VIngenjör (YH), byggnads- och samhällsteknik, 2023 Vasa, dagstudier
-
BYS22D-VIngenjör (YH), byggnads- och samhällsteknik, 2022 Vasa, dagstudier
Small groups
- BYS22-K
- BYS23-P
- BYS22-P
- BYS23-K
Objective
The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.
Content
- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.
Assessment criteria, good (3)
Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.
Assessment criteria, excellent (5)
Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.
Qualifications
Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.
Enrollment
01.12.2024 - 12.01.2025
Timing
06.01.2025 - 23.02.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
Campus
Vasa, Wolffskavägen 33
Teaching languages
- Svenska
Degree programmes
- Degree Programme in Civil and Construction Engineering
- Degree Programme in Mechanical and Production Engineering
- Degree Programme in Electrical Engineering and Automation
- Degree Programme in Industrial Management
Teachers
- Ing-Britt Rögård
Teacher in charge
Kaj Rintanen
Scheduling groups
- MAP23-K (Size: 30. Open UAS: 0.)
- MAP23-D (Size: 30. Open UAS: 0.)
Groups
-
MAP23D-VIngenjör (YH), maskin- och produktionsteknik, 2023 dagstudier
Small groups
- MAP23-K
- MAP23-D
Objective
The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.
Content
- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.
Assessment criteria, good (3)
Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.
Assessment criteria, excellent (5)
Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.
Qualifications
Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.
Enrollment
01.12.2023 - 07.01.2024
Timing
01.01.2024 - 25.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
Campus
Vasa, Wolffskavägen 33
Teaching languages
- Svenska
Degree programmes
- Degree Programme in Civil and Construction Engineering
- Degree Programme in Mechanical and Production Engineering
- Degree Programme in Electrical Engineering and Automation
- Degree Programme in Industrial Management
Teachers
- Ing-Britt Rögård
Teacher in charge
Kaj Rintanen
Groups
-
MAP22D-VIngenjör (YH), maskin- och produktionsteknik, 2022 dagstudier
Objective
The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.
Content
- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.
Assessment criteria, good (3)
Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.
Assessment criteria, excellent (5)
Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.
Qualifications
Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.
Enrollment
15.06.2023 - 03.09.2023
Timing
28.08.2023 - 08.10.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
Campus
Vasa, Wolffskavägen 33
Teaching languages
- Svenska
Degree programmes
- Degree Programme in Civil and Construction Engineering
- Degree Programme in Mechanical and Production Engineering
- Degree Programme in Electrical Engineering and Automation
- Degree Programme in Industrial Management
Teachers
- Ing-Britt Rögård
- Sofia Frilund
Teacher in charge
Ronnie Sundsten
Scheduling groups
- ELA22-S (Size: 30. Open UAS: 0.)
- ELA22-Y (Size: 30. Open UAS: 0.)
Groups
-
ELA22D-VIngenjör (YH), el- och automationsteknik, 2022, dagstudier
Small groups
- ELA22-S
- ELA22-Y
Objective
The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.
Content
- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.
Assessment criteria, good (3)
Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.
Assessment criteria, excellent (5)
Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.
Qualifications
Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.