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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
  • AUTE23KA
    Degree 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
  • AUTE23SA
    Degree 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
  • TITE23
    Bachelor 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
  • AUTE22KA
    Degree 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
  • AUTE22SA
    Degree 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