Geometry and VectorsLaajuus (3 cr)
Code: TKV22MA02
Credits
3 cr
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Qualifications
No prerequisites
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Enrollment
15.06.2025 - 20.02.2026
Timing
17.02.2026 - 10.03.2026
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Sofia Frilund
Teacher in charge
Matts Nickull
Groups
-
ÖH25FLEXINGÖppna YH, Flexibelt till Ingenjör
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2025 - 09.11.2025
Timing
03.11.2025 - 14.12.2025
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Ing-Britt Rögård
- Sofia Frilund
Teacher in charge
Kaj Rintanen
Scheduling groups
- MAP25-S (Size: 40. Open UAS: 0.)
- MAP25-Y (Size: 40. Open UAS: 0.)
- PRE25-S (Size: 40. Open UAS: 0.)
- PRE25-Y (Size: 40. Open UAS: 0.)
Groups
-
MAP25D-VIngenjör (YH), maskin- och produktionsteknik, 2025 dagstudier
-
PRE25D-VIngenjör (YH), produktionsekonomi, 2025 dagstudier
Small groups
- MAP25-S
- MAP25-Y
- PRE25-S
- PRE25-Y
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2025 - 26.10.2025
Timing
27.10.2025 - 21.12.2025
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Kennet Tallgren
Teacher in charge
Leif Östman
Groups
-
BYS25D-VIngenjör (YH), byggnads- och samhällsteknik, 2025 Vasa, dagstudier
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2025 - 09.11.2025
Timing
27.10.2025 - 14.12.2025
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Ing-Britt Rögård
Teacher in charge
Anders Ahlbäck
Groups
-
BYL25D-VIngenjör (YH), lantmäteriteknik, 2025 dagstudier
-
BYB25D-VByggmästare (YH), h25, dagstudier, Vasa
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2025 - 19.10.2025
Timing
20.10.2025 - 30.11.2025
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Sofia Frilund
- Lina Åberg
Teacher in charge
Ronnie Sundsten
Scheduling groups
- ELA25-S (Size: 50. Open UAS: 0.)
- ELA25-Y (Size: 50. Open UAS: 0.)
Groups
-
ELA25D-VIngenjör (YH), el- och automationsteknik, 2025, dagstudier
Small groups
- ELA25-S
- ELA25-Y
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2025 - 19.10.2025
Timing
20.10.2025 - 30.11.2025
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Lina Åberg
Teacher in charge
Kaj Wikman
Groups
-
UIT25D-VIngenjör (YH), informationsteknik, 2025
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 18.02.2025
Timing
19.02.2025 - 12.03.2025
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Sofia Frilund
Teacher in charge
Matts Nickull
Groups
-
ÖH24FLEXINGÖppna YH, Flexibelt till Ingenjör
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 10.11.2024
Timing
11.11.2024 - 22.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Ing-Britt Rögård
Teacher in charge
Niklas Kallenberg
Scheduling groups
- PRE24-Y (Size: 40. Open UAS: 0.)
- PRE24-S (Size: 40. Open UAS: 0.)
Groups
-
PRE24D-VIngenjör (YH), produktionsekonomi, 2024 dagstudier
Small groups
- PRE24-Y
- PRE24-S
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 10.11.2024
Timing
11.11.2024 - 22.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Ing-Britt Rögård
- Sofia Frilund
Teacher in charge
Kaj Rintanen
Scheduling groups
- MAP24-Y (Size: 40. Open UAS: 0.)
- MAP24-S (Size: 40. Open UAS: 0.)
Groups
-
MAP24D-VIngenjör (YH), maskin- och produktionsteknik, 2024 dagstudier
Small groups
- MAP24-Y
- MAP24-S
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 10.11.2024
Timing
04.11.2024 - 22.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Ing-Britt Rögård
Teacher in charge
Sem Timmerbacka
Groups
-
BYB24D-VByggmästare (YH), h24, dagstudier, Vasa
-
BYL24D-VIngenjör (YH), lantmäteriteknik, 2024 dagstudier
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 03.11.2024
Timing
04.11.2024 - 22.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Kennet Tallgren
Teacher in charge
Leif Östman
Groups
-
BYS24D-VIngenjör (YH), byggnads- och samhällsteknik, 2024 Vasa, dagstudier
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 10.11.2024
Timing
28.10.2024 - 08.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Lina Åberg
- Sofia Frilund
Teacher in charge
Ronnie Sundsten
Scheduling groups
- ELA24-Y (Size: 50. Open UAS: 0.)
- ELA24-S (Size: 50. Open UAS: 0.)
Groups
-
ELA24D-VIngenjör (YH), el- och automationsteknik, 2024, dagstudier
Small groups
- ELA24-Y
- ELA24-S
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
15.06.2024 - 27.10.2024
Timing
28.10.2024 - 08.12.2024
Number of ECTS credits allocated
3 cr
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
- Degree Programme in Land Surveying
Teachers
- Lina Åberg
Teacher in charge
Kaj Wikman
Groups
-
UIT24D-VIngenjör (YH), informationsteknik, 2024
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites
Enrollment
01.12.2023 - 18.02.2024
Timing
13.02.2024 - 05.03.2024
Number of ECTS credits allocated
3 cr
Mode of delivery
Contact teaching
Unit
Faculty of Technology and Seafaring
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
- Degree Programme in Land Surveying
Teachers
- Sofia Frilund
Teacher in charge
Matts Nickull
Groups
-
ÖH23FLEXINGÖppna YH, Flexibelt till Ingenjör
Objective
The student :
- is able to solve every kind of triangle ( both right angled triangles and others )
- is able to calculate areas and volumes of figures and solids
- is able to perform calculations with two-dimensional vectors and three-dimensional vectors.
- is familiar with matrices and masters simply calculations with matrices
Content
- Right angled triangles
- Basic trigonometric functions (cosine, sine and tangent)
- Angle units (degrees vs radians)
- The sine and cosine formula
- Uniformity and scales
- Area- and volume caculations
- Definition of the vector concept
- Rules for vector operations
- Dot product
- Projections
- Cross product
- Introduction to matrices
- MatchCad exercises
Application according to specific education may occur.
Evaluation scale
H-5
Assessment criteria, satisfactory (1)
Trigonometry: Master the trigonometry of right angled triangles
Area and volume calculations: Can calculate areas and volumes of simple figures and bodies
Vectors: Can perform calculations with two-dimensional vectors
Matrices: Knows matrices and can perform simple calculations with them
Models and problem solving: Have some understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, good (3)
Trigonometry: Master the trigonometry of any triangle
Area and volume calculations: Can calculate areas and volumes for more complicated figures and bodies
Vectors: Can do basic calculations with three-dimensional vectors
Matrices: Is able to calculate the value of a determinant
Models and problem solving: Have a good understanding of how to use a mathematical model and how it can be solved.
Assessment criteria, excellent (5)
Trigonometry: Can apply the theory for solving more complicated problems
Area and volume calculations: Can calculate areas and volumes for figures and bodies using vectors
Vectors: Can apply vectors to more complicated problems and master the use of vectors in software programs.
Matrices: Master the use of matrices in software programs
Models and problem solving: Can apply mathematical models to technical problems.
Qualifications
No prerequisites