Differential and Integral CalculusLaajuus (5 cr)
Code: 8B00CZ17
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Qualifications
No previous studies are required
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Materials
Material distributed by the lecturer
Enrollment
11.11.2024 - 15.01.2025
Timing
07.01.2025 - 27.04.2025
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Student groups
-
BIELI24Bachelor of Engineering, Food Processing and Biotechnology, Full-time studies
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 45 h and independent work 90 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required
Enrollment
22.04.2024 - 04.09.2024
Timing
26.08.2024 - 18.12.2024
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Student groups
-
MBIELI24Bachelor of Engineering, Food Processing and Biotechnology, Part-time studies
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 20 h and independent work 115 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required
Enrollment
13.11.2023 - 17.01.2024
Timing
08.01.2024 - 28.04.2024
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Student groups
-
BIELI23Bachelor of Engineering, Food Processing and Biotechnology, Full-time studies
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 45 h and independent work 90 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required
Enrollment
14.11.2022 - 15.01.2023
Timing
09.01.2023 - 30.04.2023
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Student groups
-
BIELI22
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 45 h and independent work 90 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required
Enrollment
16.04.2022 - 07.09.2022
Timing
12.09.2022 - 11.12.2022
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Student groups
-
MBIELI22
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 20 h and independent work 115 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required
Enrollment
19.04.2021 - 09.01.2022
Timing
10.01.2022 - 15.05.2022
Credits
5 op
Teaching languages
- Finnish
Degree programmes
- Bachelor of Engineering, Food Processing and Biotechnology
Teachers
- Heikki Kokkonen
Responsible person
Jukka Kauppila
Student groups
-
BIELI21
-
BIELI21B
-
BIELI21A
Objective
Professional part (5 ects):
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 and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.
Content
Professional part (5 ects):
- 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
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering
Materials
The learning material is in the moodle
Teaching methods
Lectures and independent work
Student workload
Lectures 45 h and independent work 90 h
Evaluation scale
1-5
Assessment criteria, satisfactory (1)
Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.
Assessment criteria, good (3)
In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.
Assessment criteria, excellent (5)
In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.
Assessment methods and criteria
exam
Qualifications
No previous studies are required