# Basics of Technical Mathematics

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

Code: | IST1002 |

Type: | Compulsory / Basic Studies |

Curriculum: | ST 2018 |

Level: | Bachelor of Engineering |

Year of Study: | 1 (2018-2019) |

Semester: | Autumn |

Credits: | 3 cr |

Responsible Teacher: | Mäkelä, Jarmo |

Language of Instruction: | Finnish |

## Courses During the Academic Year 2018-2019

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

6 | I-TT-1N | 2018-08-31 – 2018-12-21 | Jarmo Mäkelä | Finnish | 2018-08-20 – 2018-09-17 |

7 | I-ST-1N | 2018-08-31 – 2018-12-10 | Jussi Ojanen | Finnish | 2018-08-20 – 2018-09-17 |

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

## Learning Outcomes

A good mathematical knowledge is a basic requirement for engineering studies. Without a basic knowledge of mathematics is impossible to carry out the daily tasks of an engineer, and understand the professional literature. This course begins from the very basics of mathematics, and in principle it does not assume any previous knowledge in mathematics. At the beginning the student is made familiar with the natural numbers and their basic arithmetic operations. Little by little, the student is introduced to basic algebra, and to an important concept of function. The most common functions and their properties are presented to the student. An important role in the course is played by the art of solving equations, as well as systems of equations. The student is also made familiar with the basic trigonometry and -geometry.

## Student's Workload

81 h, which includes 42 h of scheduled contact studies at VAMK and 24 h at the University of Vaasa.

## Contents

The concept of set. Natural numbers and their symbols. Addition, subtraction, multiplication and division of natural numbers. Multiplication table. Addition, subtraction, multiplication and division by pen and paper. Long division. The rules of calculation and the order of the basic operations of arithmetic. Fractions and their rules of calculation. Decimal numbers and their operations. The concept of per cent, and its operations. The concepts of length, area and volume. The units of length area, and volume, together with their multiples and submultiples. The concept of litre and its relation to the other units of volume. Negative numbers and their rules of calculation. Basic algebra: real numbers and their rules of calculation. Interpretation of the real numbers as the points of the number line. Powers and roots. Negative powers, Fractional powers. Rules of powering. Extraction of roots by means of pen and paper. Powers of sums and Pascal’s triangle. The concept of function. The graph of the function. Polynomials. Multiplication and division of polynomials. Rational functions. Simplification of algebraic expressions. Linear equations. Equations, which may be reduced to linear equations. Equations of the second and higher degree. Factorization of polynomials. Linear systems of equations. Solution of linear systems of equations by substitution and elimination. Exponentials. Logarithms. Rules of calculation of logarithms. Natural logarithm. Calculation of natural logarithms by means of power series. Plain geometry: Triangle and circle. The areas of the triangle and the circle, and the circumference of the circle. The concept of angle. Pyrthagoras’s theorem. The volmes and the areas of the sphere , the cylinder and the cone. Trigonometric functions defined by means of the properties of the right triangle. The basisc properties of trigonometric functions. The sine rule and the cosine rule. Calculation of the sine and the cosine of the given angle by means of power series. Calculation of the unknown edge lengths and the angles of the given triangle. Analytic geometry: Plane, circle and parabola. The slope of a line, and the determination of the equation of the line passing through two points. Orthogonal lines. The equation of the circle. The tangent of the circle. The focus and the directrix of the parabola. The equations of the ellipse and the hyperbola.

## 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.