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# Introduction to Technical Mathematics

Structure Type: Study unit IXP0411 TT 2020V Bachelor of Engineering 1 (2020-2021) Autumn 4 cr Ojanen, Jussi Finnish

## Courses During the Academic Year 2020-2021

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3001ST2020V-1, ST2020V-1A, ST2020V-1B, TT2020V-1A2020-08-24 – 2020-10-18Jarmo MäkeläFinnish2020-08-17 – 2020-09-11

## Learning Outcomes

The student learns the basics of arithmetic, algebra and geometry. She can add, subtract, multiply, and divide integers, fractions and reals. She knows the concepts of power and root of a real number, and she can apply their rules of calculation. She understands what is meant by the concepts of function and the graph of a function, and she knows the elementary functions, like polynomial, exponential, and logarithmic functions. The student learns the basics of symbolic calculations performed with real numbers, and she can solve simple equations and systems of equations. In plane geometry the student learns the basic properties of rectangles, triangles, circles and parallellograms. She learns the basics of trigonometry, and she can calculate the angles and the edge lengths of a given triangle. In space geometry the student is made familiar with the concepts of sphere, cone and cylinder. In analytic geometry the student learns the basic properties of line, parabola and circle.

The total amount of student's work is 108 h, which contains 44 h of scheduled contact studies. The assessment of student’s own learning 1 h is included in contact lessons.

## Prerequisites / Recommended Optional Courses

Secondary education mathematics.

## Contents

Positive and negative integers, fractions and reals, together with their addition, subtraction, multiplication and division. Powering and extraction of roots. Function and its graph. Polynomials, exponentials and logarithms. Basics of symbolic calculations with real numbers. Linear and quadratic equations and systems of equations. Numerical solution of equations with grade higher than two by means of iteration, together with methods of finding exact solutions in some special cases. Factorization of polynomials, and simplification of rational expressions. Basic properties of rectangles, triangles, circles and parallelograms. Trigonometric functions defined by means of a right triangle. Finding edge lengths and angles of an arbitrary triangle by means of the sine and the cosine rules. Spheres, cylinders and cones. The equations of a line, a parabola and a circle in xy coordinates, together with their basic properties.

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

Majaniemi: "Algebra I ja II" and "Geometria", Tietokotka Oy; 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. An essential ingredient of learning, however, consists of exercises which are gone through during the lectures, and independent homework performed by the student. 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.

## Assessment Criteria

Grade 5: The student is able to apply creatively the contents of the course.
Grade 3: The student is well-abled to utilize the course contents.
Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.

## Assessment Methods

Two examinations, homework exercises and tutored exercise sessions. The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. At least 25 % of the given homework exercises must be solved in order to pass the course.