# Differential Calculus

Rakennetyyppi: | Opintojakso |
---|---|

Koodi: | IITB3003 |

OPS: | IT 2021 |

Taso: | Insinööri (AMK) |

Opiskeluvuosi: | 2 (2022-2023) |

Lukukausi: | Syksy |

Laajuus: | 2 op |

Vastuuopettaja: | Mäkelä, Jarmo |

Opetuskieli: | Englanti |

## Toteutukset lukuvuonna 2022-2023

Tot. | Ryhmä(t) | Opiskeluaika | Opettaja(t) | Kieli | Ilmoittautuminen |
---|---|---|---|---|---|

3003 | IT2021-2, IT2021-2A, IT2021-2B | 29.8.2022 – 15.10.2022 | Jarmo Mäkelä | Englanti | 1.8.2022 – 6.9.2022 |

## Osaamistavoitteet

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.

## Opiskelijan työmäärä

54 h, which contains 28 h of scheduled contact studies.

The assessment of student’s own learning 1 h is included in contact lessons.

## Sisältö

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.

## Opiskelumateriaali

Material prepared by the teacher.

## Opetusmuoto / Opetusmenetelmät

Lectures, exercises.

## Arviointikriteerit

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.

## Arviointimenetelmät

Homework exercises, assignments, an examination.