# Analysis

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

Koodi: | ET00BN21 |

OPS: | ETE 2024 |

Taso: | Insinööri (AMK) |

Opiskeluvuosi: | 2 (2025) |

Lukukausi: | Kevät |

Laajuus: | 5 op |

Vastuuopettaja: | Pyhälahti, Onni |

Opetuskieli: | Englanti |

Suoritus ennakkoon? Katso toteutukset lukuvuonna 2023-2024.

## Osaamistavoitteet

The course introduces differential calculus and integral calculus. In addition, sequences and series are introduced.

After the course the students know the following concepts and are able to apply them to practice.

Differential Calculus:

Limit of a function, continuity, derivatives of first and higher degrees, derivatives of elementary functions, understanding derivative as a slope of the tangent and how it indicates the change rate of a quantity, function differential and error estimation, derivative of a product, derivative of a quotient, derivative of a composite function, the concept of extremum

Integral Calculus:

the concept of the integral applying it for the calculation of areas and volumes, solving simple differential equations

Basics of sequences and series.

## Opiskelijan työmäärä

The total amount of student's work is 135h, which contains 45 h of contact studies and 90 h of student's own work outside classroom.

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

## Edeltävät opinnot / Suositellut valinnaiset opinnot

Introduction to Tehcnical mathematics

Numerical Mathematics

## Sisältö

Differential calculus:

Limit of a function and derivatives, derivatives of elementary functions, composite function, partial derivative, total differential, extremums of a one variable function. Engineering applications.

Integral Calculus:

Integral, integrations methods of functions, calculation of areas, volumes and length of curves and numerical integration. Solving differential equations by separation of variables, applications.

Arithmetical progressions and geometrical series and basics of power series.

## Opetusmuoto / Opetusmenetelmät

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 exercises in groups and independently at home.

## Arviointikriteerit

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

## Arviointimenetelmät

Examination and homework exercises.

The number of completed exercises affects the grade.