Integral Calculus
| Structure Type: | Study unit |
|---|---|
| Code: | IST4001 |
| Type: | Compulsory / Basic Studies |
| Curriculum: | ST 2016 / 2017 / 2018 / 2019 / 2020 / 2021 TT 2016 / 2017 / 2018 / 2019 / 2020 / 2021 |
| Level: | Bachelor of Engineering |
| Year of Study: | 1 / 2 (2016-2017 / 2017-2018 / 2018-2019 / 2019-2020 / 2020-2021 / 2021-2022 / 2022-2023) |
| Credits: | 2 cr |
| Responsible Teacher: | Mäkelä, Jarmo |
| Language of Instruction: | Finnish |
Courses
| Impl. | Group(s) | Study Time | Teacher(s) | Language | Enrolment |
|---|---|---|---|---|---|
| 1 | I-ST-2N | 2017-09-01 – 2017-10-27 | Jussi Ojanen | Finnish | 2017-08-23 – 2017-09-18 |
| 2 | I-TT-2N | 2018-01-08 – 2018-02-23 | Jarmo Mäkelä | Finnish | 2017-12-11 – 2018-01-15 |
| 3 | I-ST-2N | 2018-08-31 – 2018-11-02 | Jussi Ojanen | Finnish | 2018-08-20 – 2018-09-17 |
| 4 | I-TT-2N, YHT-VY-1 | 2019-01-07 – 2019-04-10 | Jarmo Mäkelä | Finnish | 2018-12-10 – 2019-01-14 |
| 5 | I-ST-2N | 2019-09-02 – 2019-12-20 | Jussi Ojanen | Finnish | 2019-08-19 – 2019-09-09 |
| 6 | I-TT-2N, YHT-VY-1 | 2020-01-07 – 2020-02-21 | Jarmo Mäkelä | Finnish | 2019-12-16 – 2020-01-14 |
| 3001 | VY-1 | 2021-01-04 – 2021-02-28 | Jarmo Mäkelä | Finnish | 2020-08-17 – 2021-01-10 |
| 3002 | ST2019-2, ST2019-2A, ST2019-2B, ST2019-2C, ST2019-2D | 2020-08-24 – 2020-12-20 | Jarmo Mäkelä | Finnish | 2020-08-17 – 2020-09-11 |
| 3003 | TT2020-2A, TT2020-2B, TT2020-2C, TT2020-2D, VY-1 | 2022-01-03 – 2022-02-27 | Jarmo Mäkelä, Seppo Mäkinen | Finnish | 2021-12-01 – 2022-01-10 |
| 3004 | ST2020-2, ST2020-2A, ST2020-2B, ST2020-2C, ST2020-2D | 2021-08-23 – 2021-12-19 | Jussi Ojanen | Finnish | 2021-08-01 – 2021-09-06 |
| 3016 | TT2021-2, TT2021-2A, TT2021-2B, TT2021-2C, TT2021-2D | 2023-01-09 – 2023-04-29 | Jarmo Mäkelä | Finnish | 2022-12-01 – 2023-01-10 |
| 3017 | ST2021-2, ST2021-2A, ST2021-2B, ST2021-2C, ST2021-2D | 2023-01-09 – 2023-02-25 | Lassi Lilleberg | Finnish | 2022-12-01 – 2023-01-10 |
The descriptions shown below are for the academic year: 2022-2023
Learning Outcomes
The integral of a function gives an answer to the question: Which is the function, whose derivative the given function is? For example, (one of) the integral function(s) of 2x is x^2, since the derivative of x^2 is 2x. The integral can be used, for example, in evaluating surface areas and volumes, and it is useful in studying the average behaviour of a function in a given time interval. In this course, the student learns to evaluate integral functions of some given functions, and she will learn how to apply integral calculus for, e.g., determining areas and volumes.
Student's Workload
54 h, which contains 28 h of scheduled contact studies at VAMK and 16 h at UVA.
Contents
A short revision of differential calculus. The integral function. Integral function of the power function, the exponent function and the trigonometric functions. Integral of the sum. Definite integral and its interpretation as the surface area. The area enclosed by two plane curves. Integration by parts. Integration by substitution (changing the variable). Integrating a rational function by partial fractions. The average value and the root-mean-square value of a function. The length of a plane curve. The surface area and the volume of a solid of revolution. The center of mass of a homogenous planar object. Numerical integration by polynomial fitting and by Simpson’s rule.
Recommended or Required Reading and Other Learning Resources/Tools
P. Lehtola, A. Rantakaulio: Tekninen matematiikka 2, Tammertekniikka. Material prepared by the teacher.
Mode of Delivery / Planned Learning Activities and Teaching Methods
Lectures, exercises.
Assessment Criteria
Grade 5: The student is able to solve problems creatively in almost all the contents of the course.
Grade 3: The student can solve applied problems related with the central contents of the course.
Grade 1: The student can solve basic problems on the central contents of the course.
Assessment Methods
Homework exercises, assignments, an examination.