Differential and Integral CalculusLaajuus (3 cr)
Code: KC00AMT1020
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Qualifications
Algebra and geometry, Vectors and matrices
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Materials
To be announced at the beginning of the course
Enrollment
22.04.2024 - 09.10.2024
Timing
21.10.2024 - 18.12.2024
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE23KADegree Programme in Automation Engineering, Full-time studies
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises + exam
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
22.04.2024 - 09.10.2024
Timing
21.10.2024 - 18.12.2024
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE23SADegree Programme in Automation Engineering, Full-time studies
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises + exam
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
22.04.2024 - 04.09.2024
Timing
26.08.2024 - 13.10.2024
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Information Technology
Teachers
- Pasi Mikkonen
Student groups
-
TITE23Bachelor of Engineering, Information Technology
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises + exam
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
17.04.2023 - 15.10.2023
Timing
23.10.2023 - 17.12.2023
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE22KADegree Programme in Automation Engineering, Full-time studies
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
17.04.2023 - 11.10.2023
Timing
23.10.2023 - 17.12.2023
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE22SADegree Programme in Automation Engineering, Full-time studies
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
17.04.2023 - 06.09.2023
Timing
28.08.2023 - 15.10.2023
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Information Technology
Teachers
- Pasi Mikkonen
Student groups
-
TITE22
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
16.04.2022 - 12.10.2022
Timing
24.10.2022 - 18.12.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Information Technology
Teachers
- Pasi Mikkonen
Student groups
-
TITE21
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
16.04.2022 - 07.09.2022
Timing
29.08.2022 - 16.10.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE21KA
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
16.04.2022 - 07.09.2022
Timing
29.08.2022 - 16.10.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Jyrki Parkkinen
Student groups
-
AUTE21SA
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises and final exam
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
16.04.2022 - 07.09.2022
Timing
15.08.2022 - 16.10.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
MAUTE21
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
03.12.2021 - 23.01.2022
Timing
10.01.2022 - 27.02.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE20KA
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices
Enrollment
03.12.2021 - 23.01.2022
Timing
10.01.2022 - 27.02.2022
Credits
3 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Automation Engineering
Teachers
- Pasi Mikkonen
Student groups
-
AUTE20SA
Objective
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.
Content
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)
Materials
to be announced
Teaching methods
lectures and exercises, independent study
Student workload
81h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.
Assessment criteria, good (3)
good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject
Assessment criteria, excellent (5)
excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.
Assessment methods and criteria
exercises
Qualifications
Algebra and geometry, Vectors and matrices