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# Analytic Geometry and Linear Algebra

Structure Type: Study unit IXP0402 TT 2020V Bachelor of Engineering 1 (2020-2021) Spring 2 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-1A2021-01-04 – 2021-02-28Jussi OjanenFinnish2020-08-17 – 2021-01-10

## Learning Outcomes

The student is made familiar with matrices, vectors, trigonometry, complex numbers and inequalities. She knows the rules of calculation of matrices, and she is able to calculate the determinant of a given square matrix. She learns to calculate the inverse of a square matrix, and to apply matrices and determinants for a solution of linear systems of equations. In trigonometry she is made familiar with the concept of radian, and she understands the connection between trigonometric functions and the coordinates of a point of a unit circle correponding to a given angle, together with the basic properties of trigonometric functions following from this connection. In vector calculus the sudent is made familiar with addition and substraction of vectors, together with a multiplication of a vector by a number and the component representation of a vector. In addition, the student learns the concepts of dot and cross products of vectors, and knows how to apply them in the solution of geometrical problems. The student is made familiar with complex numbers, and she can write a given complex number in a polar representation. Using the polar representation the student can multiply and divide complex numbers by each other, and to raise a complex number to a given power. The student learns to solve linear, quadratic and rational inequalities.

The total amount of student's work is 54 h, which contains 22 h of scheduled contact studies. The assessment of student’s own learning 1 h is included in contact lessons.

## Prerequisites / Recommended Optional Courses

Introduction to Technical Mathematics.

## Contents

Matrices, determinats, and their appplications for the solution of linear systems of equations. Trigonometric functions defined by means of the coordinates of the points of a unit circle. The concept of radian. Basic properties of trogonometric functions, graphs of trigonometric functions, and trigonometric equations. Vectors, their component representation, and dot and cross products. Applications of vector calculus for a solution of simple geometric propblems. Complex numbers, their basic properties and the polar representation. Multiplication, division and powering of complx numbers in a polar representation. Linear, quadratic and rational inequatlities.

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

Majaniemi: "Algebra I ja II" and "Geometria", 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. 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

An exam, 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 passt the course.