# Differential Calculus

Structure Type: | Study unit |
---|---|

Code: | IXP0403 |

Curriculum: | TT 2020V |

Level: | Bachelor of Engineering |

Year of Study: | 1 (2020-2021) |

Semester: | Spring |

Credits: | 2 cr |

Responsible Teacher: | Ojanen, Jussi |

Language of Instruction: | Finnish |

## Courses During the Academic Year 2020-2021

Impl. | Group(s) | Study Time | Teacher(s) | Language | Enrolment |
---|---|---|---|---|---|

3001 | ST2020V-1, ST2020V-1A, ST2020V-1B, TT2020V-1A | 2021-03-01 – 2021-05-02 | Jarmo Mäkelä | Finnish | 2020-08-17 – 2021-01-10 |

## 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.

## Student's Workload

The total amount of student's work is 54 h, which contains 22 h of scheduled contact studies. The assessment of student’s own learning 1 h is included in contact lessons.

## Prerequisites / Recommended Optional Courses

Analytic Geometry and Linear Algebra.

## 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

P. Lehtola, A. Rantakaulio: Tekninen matematiikka 2, Tammertekniikka. 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. At the end of the course, students may be given exercises which are to be solved with a computer.

## 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

An examination, homework exercises and tutored exercise sessions. The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. All the given computer-related exercises must be handed in by the end of the course. At least 25 % of the given homework exercises must be solved in order to pass the course.