# Numerical Mathematics

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

Code: | IK00BE73 |

Curriculum: | YT 2023 |

Level: | Bachelor of Engineering |

Year of Study: | 1 (2023-2024) |

Semester: | Spring |

Credits: | 5 cr |

Responsible Teacher: | Pyhälahti, Onni |

Language of Instruction: | Finnish |

## Courses During the Academic Year 2023-2024

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

3013 | YT2023-1, YT2023-1A, YT2023-1B | 2024-01-08 – 2024-04-30 | Elena Kuisma | Finnish | 2023-12-01 – 2024-01-12 |

3017 | ET2023-1, ET2023-1A, ET2023-1B | 2024-01-08 – 2024-04-30 | Elena Kuisma | Finnish | 2023-12-01 – 2024-01-12 |

3018 | KT2023-1, KT2023-1A, KT2023-1B, KT2023-1C, KT2023-1D | 2024-01-08 – 2024-04-27 | Onni Pyhälahti | Finnish | 2023-12-01 – 2024-01-12 |

3019 | KT2023V-1, KT2023V-1A, KT2023V-1B | 2024-01-08 – 2024-05-25 | Kerstin Siegfrids | Finnish | 2023-12-01 – 2024-01-12 |

3020 | EY2023V-1, EY2023V-1A, EY2023V-1B | 2024-01-08 – 2024-05-25 | Onni Pyhälahti | Finnish | 2023-12-01 – 2024-01-12 |

## Learning Outcomes

The student is introduced to matrix calculus, as well as trigonometry and complex numbers. The objective is that the student can solve systems of equations where the factors are complex numbers. In addition, the student knows the various representations of complex numbers. The student can also solve simple inequalities and knows the properties of second order curves.

The student will learn to use mathematical software to solve tecnical-mathematical problems. These programs can be used both for numerical and symbloical calculations and to plot graphs etc.

During this course a student learns the basics of the theory of probability and statistics. S/he knows how to sample using random numbers and understands the uncertainty factors related to samples and sample studies. S/he can work the material using a computer and present the data graphically, interpret statistic charts made by others and calculate parametres related to material and find out dependencies between variables. S/he understands the calculation rules of probability and knows the importance of probability as an interpreter of statistical significance. S/he learns to use the most important distributions with a computer and can complete basic statistical tests and calculate confidential intervals.

## Student's Workload

The total amount of student's work is 135h, which contains 50 h of contact studies and 85 h of student's own work outside classroom.

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

## Prerequisites / Recommended Optional Courses

Introduction to Tehcnical mathematics

## Contents

Trigonometric formulae and equations, complex numbers, second degree curves in the plane, determinants and basics of matrix calculus, inequalities.

Short overview to mathematical software: basic operations, functions and graphs, units, vectors, curve fitting, solving equations and systems of equations, symbolic calculation.

Collecting and processing statistical data, graphic representation and drawing conclusions. Calculation of indexes, probability calculation rules and probability distributions. Regression lines and correlation coefficient. Estimation of parametres, confidential intervals and average tests.

Applications on the field of engineering.

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

S. Alestalo, P. Lehtola, T. Nieminen, A. Rantakaulio: Tekninen matematiikka 1, Tammertekniikka

Seppo Mäkinen: VirtuaaliAnkka.exe, VAMK

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 exercises together with others and independently at home.

## 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

Examination and homework exercises. The number of completed exercises affects the grade.