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# Differential Calculus

Structure Type: Study unit IKTP0111 Compulsory / Basic Studies YT 2019 Bachelor of Engineering 2 (2020-2021) Autumn 2 cr Niemelä, Riitta Finnish

## Courses During the Academic Year 2020-2021

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3001KT2019-2, KT2019-2A, KT2019-2B2020-09-01 – 2020-12-31Kerstin SiegfridsFinnish2020-08-17 – 2020-09-11
3002ET2019-2, ET2019-2A, ET2019-2B, YT2019-2, YT2019-2A, YT2019-2B2020-10-19 – 2020-12-20Kerstin SiegfridsFinnish2020-08-17 – 2020-09-11

## Learning Outcomes

After the study unit the student knows the following concepts and can apply them in own field of study: limit of a function, continuity and derivatives of 1st or higher order. The student can derivate the most common elementary functions, knows the significance of the derivative as a slope of a tangent line and as an expresser of conversion rate of a quantity, knows the differential of a function and its use in error assessment , knows the product and quotient of the derivative and composite function, knows the concept of extremum and can apply it.

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

## Contents

Limit and derivative, derivation of basic functions, composite function and study of functions. Partial derivative, total differential, extremums of single-variable functions. Application related to engineering.

## 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 problems in groups at rehearsals and independently at home.

## 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

An examination, exercises in exercise sessions.

The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. The given self assesment must be handed in by the end of the course.