# Teknillisen matematiikan jatkokurssi

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

Code: | TT00BI63 |

Curriculum: | TT 2023 |

Level: | Bachelor of Engineering |

Year of Study: | 2 (2024-2025) |

Semester: | Autumn |

Credits: | 5 cr |

Responsible Teacher: | Mäkelä, Jarmo |

Language of Instruction: | Finnish |

Taking the course in advance? See the courses during the academic year 2023-2024.

## Learning Outcomes

At the end of the course the student possesses basic knowledge about differential and integral calculus of single-variable functions, differential equations and series.

## Student's Workload

The total work load of the student in the course is around 130 work hours.

## Prerequisites / Recommended Optional Courses

Basics of Technical Mathematics

## Contents

1) LImit and continuity of a function. 2) The derivative of a function and its geometrical interpretation. 3) Rules of differentiation. 4) Partial derivative and differentiation. 5) Optimization. 6) Indefinite integral. 7) Definite integral and its geometrical interepretation. 8) Methods of integration: Integration by parts, integration by substitution. 9) The volume of the solid of revolution. 10) Center of gravity of a plate. 11) First-order differential equations. 12) Second-order differential equation with constant coefficients. 13) Laplace transform. 14) Inverse Laplace transform. 15) Solution of limear differential equations by means of Laplace transforms. 16) Series: Arithmetic and geometrical series. 17) Power series: Maclaurin series. 18) Binomial series. 19) Evaluation of definite integrals by means of power series.

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

The material given by the lecturer during the lectures. Useful additional material may be found in the books written by A. Majaniemi: Matematiikka I, II, III. They may be downloaded from the Internet for free.

## Mode of Delivery / Planned Learning Activities and Teaching Methods

The course consists of lectures and exercises associated with the lectures.

## Assessment Criteria

The possible grades obtainable from the course are 1, 2, 3, 4, 5.

1: The student knows the basic concepts of the course

2: The student knows about one-half of the topics taught on the course, and is able to solve simple problems

3: The student is able to solve pretty challenging problems and knows the concepts of the course

4: The student knows more or less the topics learned in the course

5: The student knows everything taught in the course.

## Assessment Methods

There will be two examinations in the course. The grade of the course is determined by the total number of points obtained from the exams. In addition, the student must solve the given number number of exercise problems.