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# Integral Calculus

Structure Type: Study unit IST4001 Compulsory / Basic Studies ST 2018 Bachelor of Engineering 1 (2018-2019) Spring 2 cr Mäkelä, Jarmo Finnish

## Courses During the Academic Year 2018-2019

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3I-ST-2N2018-08-31 – 2018-11-02Jussi OjanenFinnish2018-08-20 – 2018-09-17
4I-TT-2N, YHT-VY-12019-01-07 – 2019-04-10Jarmo MäkeläFinnish2018-12-10 – 2019-01-14

Still need to take the course? See the courses during the academic year 2021-2022.

## 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.

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.