# Analysis

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

Code: | IRTP0212 |

Type: | Compulsory / Basic Studies |

Curriculum: | KT 2016V |

Level: | Bachelor of Engineering |

Year of Study: | 2 (2017-2018) |

Credits: | 2 cr |

Responsible Teacher: | Niemi, Henry |

Language of Instruction: | Finnish |

## Courses During the Academic Year 2017-2018

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

5 | I-KT-2V | 2017-08-25 – 2017-10-27 | Sanna Rintala | Finnish | 2017-08-21 – 2017-09-18 |

Still need to take the course? See the courses during the academic year 2019-2020.

## Learning Outcomes

Analysis is straight forward continuation for the differential calculus course, and in this course the student gets the basic knowledge of integral calculus, differential equations and series. Using integral calculus one may calculate, among other things areas of planar regions and volumes of solids. Differential equations, in turn, has applications in various branches of engineering. By means of differential equations one may investigate, the changes in the electric current and voltage in an electric circuit as a function of time. Actually, most of the equations used in the appplications of mathematics are differential equations. Series, in turn, are needed, when the behavious of a function is hopelessly complicated, and one needs a practical approximation of the behavior of the function within some small domain. In this course the student learns to integrate, solve differential equations and to write the power series of the given function, as well to apply the things learned. In addition, engineering students are made familiar with Fourier series, which play an important role, among other things, in a mathematical analysis of oscillations. The sudent is also made familiar with

Z transforms and difference equations.

## Student's Workload

The total amount of student's work is 54 h, which contains 20 h of contact studies.

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

## Prerequisites / Recommended Optional Courses

Differential Calculus

## Contents

Definite and indefinite integrals, formulas of integration, area and volume, numerical integration. Basic concepts of differential equations. Separation of variables and a linear differential equation. Differential equations of the second order with constant coefficients. Sequences, numerical solution of differential equations. Arithmetical and geometrical series. Power series and their applications. Fundamentals of Fourier series. Applications specific to degree programme.

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

Majaniemi: "Matematiikka I, II and III", Tietokotka Oy; 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 independently, at home, the problems given by the lecturer. Solutions to the problems are given during the lectures. Students are given exercises which are to be solved with a computer.

## 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

Exercises and examination. The student is required to perform at least one quarter of the homework exercises. All the given computer-related exercises must be handed in by the end of the course.