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# Differential Calculus

Structure Type: Study unit IITB3003 IT 2021 Bachelor of Engineering 2 (2022-2023) Autumn 2 cr Mäkelä, Jarmo English

## Courses During the Academic Year 2022-2023

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3003IT2021-2, IT2021-2A, IT2021-2B2022-08-29 – 2022-10-15Jarmo MäkeläEnglish2022-08-01 – 2022-09-06

## Learning Outcomes

Differential calculus is based on the concept of derivative of a function. In short, the derivative of a function may be calculated, if we divide the change taken by the function by the corresponding change taken by its variable, when the change in the variable is small. The fuel consumption of an automobile, for instance, increases together with its speed, and the increase in the fuel consumption divided by the increase in the speed gives the derivative of the fuel consumption with respect to the speed. The derivative of a function is one of the most important concepts of the whole mathematics, and almost all formulas of the engineering sciences have been written by means of it. In this course one learns to differentiate functions, and to apply the concept of derivative, among other things, to optimization.

54 h, which contains 28 h of scheduled contact studies.
The assessment of student’s own learning 1 h is included in contact lessons.

## Contents

The limit of a function at a point and at infinity. Continuous functions. The derivative of a function. Interpretation of derivative as the slope of the tangent. Derivatives of powers, logarithms, exponentials, and trigonometric functions. Logarithmic differentiation. Rules of differentiation for the sum, product, quotient, and composite functions. Higher derivatives. Application of differentiation for optimization. Local extrema of a function.

## Recommended or Required Reading and Other Learning Resources/Tools

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.