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# Differential and Integral Calculus

Structure Type: Study unit IKTP0308 Compulsory / Basic Studies KT 2014 Bachelor of Engineering 3 (2016-2017) 3 cr Elomaa, Virpi Finnish

## Courses During the Academic Year 2016-2017

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
11I-KT-2N2017-01-09 – 2017-04-30Onni PyhälahtiFinnish2016-12-12 – 2017-01-16

## Learning Outcomes

After the study unit the student knows the following concepts and can apply them in mechanical engineering: limit of a function, continuity, 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 integral as a concept and is able to apply it to calculate areas, volumes and length of curves. In addition, the student can solve simple differential equations and knows the basics of series.

The total amount of student's work is 81h, which contains 42h of contact studies.

## Prerequisites / Recommended Optional Courses

Analytic Geometry and Linear Algebra

## Contents

Limit and derivative, derivation of basic functions, composite function, study of functions. Partial derivative, total differential, extremums of single-variable functions.
Integral, integrations methods of functions, calculation of areas, volumes and legnth 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

Majaniemi: "Matematiikka I, II and III", Tietokotka Oy; 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 independently, at home, the problems given by the lecturer. Solutions to the problems are given during the lectures. Students are given exercises which are to be solved with a computer.

## 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 perform at least one quarter of the homework exercises. All the given computer-related exercises must be handed in by the end of the course.