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Integral Calculus

Structure Type: Study unit
Code: IKTP0112
Type: Compulsory / Basic Studies
Curriculum: YT 2019
Level: Bachelor of Engineering
Year of Study: 2 (2020-2021)
Semester: Autumn
Credits: 2 cr
Responsible Teacher: Niemelä, Riitta
Language of Instruction: Finnish

Courses During the Academic Year 2020-2021

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3001KT2019-2, KT2019-2A, KT2019-2B2021-01-01 – 2021-03-08Onni PyhälahtiFinnish2020-08-17 – 2021-01-10
3002ET2019-2, ET2019-2A, ET2019-2B, YT2019-2, YT2019-2A, YT2019-2B2021-01-01 – 2021-03-07Onni PyhälahtiFinnish2020-08-17 – 2021-01-10

Learning Outcomes

The student understands the concept of the integral and is able to apply it for the calculation of areas and volumes. In addition, the student is able to solve simple differential equations and knows the basics of series.

Student's Workload

The total amount of student's work is 54 h, which contains 24 h of contact studies.
The assessment of student’s own learning 1 h is included.

Prerequisites / Recommended Optional Courses

Analytic Geometry and Linear Algebra
Differential Calculus


Integral, integrations methods of functions, calculation of areas, volumes and length of curves and numerical integration. Solving differential equations by separation of variables, applications. Arithmetical progressions and geometrical series and basics of power series.

Recommended or Required Reading and Other Learning Resources/Tools

P. Lehtola, A. Rantakaulio: Tekninen matematiikka 2, Tammertekniikka.

The material prepared by the teacher.

Mode of Delivery / Planned Learning Activities and Teaching Methods

The basics of learning constitutes of lectures where the theory is explained and examples are given. A mere attending the lectures and listening to the lecturer is not sufficient for proper learning. In practice, an independent pondering of the contents of the course becomes best realized when a student solves in groups at excersisses and independently at home the problems given by the lecturer.

Assessment Criteria

Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.

Grade 3: The student is well-abled to utilize the course contents.

Grade 5: The student is able to apply creatively the contents of the course.

Assessment Methods

Exercises and examination. The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. The student is required to perform at least one quarter of the homework exercises.