# Differential Equations and Series

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

Code: | IST5001 |

Type: | Compulsory / Basic Studies |

Curriculum: | ST 2018 |

Level: | Bachelor of Engineering |

Year of Study: | 2 (2019-2020) |

Semester: | Autumn |

Credits: | 2 cr |

Responsible Teacher: | Mäkelä, Jarmo |

Language of Instruction: | Finnish |

## Courses During the Academic Year 2019-2020

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

5 | I-ST-2N | 2019-10-21 – 2019-12-20 | Jussi Ojanen | Finnish | 2019-08-19 – 2019-09-09 |

6 | I-TT-2N, YHT-VY-1 | 2019-09-02 – 2020-04-24 | Jarmo Mäkelä | Finnish | 2019-12-16 – 2020-01-14 |

Still need to take the course? See the courses during the academic year 2021-2022.

## Learning Outcomes

Almost all equations in engineering are fundamentally differential equations. To put it short, a differential equation is an equation, which includes derivatives. The solution of a differential equation is a function, which satisfies the equation. In the first part of this course, the student learns to solve the most common types of differential equations. Laplace’s transformation maps a differential equation onto an algebraic equation, which can be solved relatively easily. The second part of this course introduces series, especially the power series. Almost any function relevant to engineering can be represented as a power series. Selected terms of the series constitute a polynomial, which yields an approximation to the function near a given point. Power series allows an easy way to approximate the value of a function without a computer or a pocket calculator. With the series one can also perform, e.g., numerical integrations.

## Student's Workload

54 h, which includes 28 h of scheduled contact studies at VAMK and 16 h at UVA.

## Contents

Ordinary Differential Equation. Initial conditions. Separable equations. Linear homogenous equations of the 1st order. Linear equations of the 1st order with constant coefficients. Linear equations of the 1st order, varying the constants. Linear equations of the 2nd order with constant coefficients. Laplace’s transform. Numerical methods: Euler, Runge and Kutta. Sequences. Arithmetic series. Geometric series. Power series: Taylor, Maclaurin. Numerical differentiation stencils. Fourier series. Integrating with series.

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

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