Introduction to Mathematics - Basic Course

Consolidating the knowledge and skills developed in High School. The course material covers topics, which allow developing basic mathematical competences. Extending students knowledge about functions of real variable, planar geometry and analitical geometry. Introducing basic concepts from Integral Calculus and Matrix Calculus.

Lecture

Geometric Constructions (3h/3h)

Perpendicular line, parallel line

Dividing an interval into n equal parts

Constructing selected angles

Functions of one real variable (4h/4h)

Definition of a function

Graph of a function

Properties of linear and quadratic functions

Properties of trigonometric functions

Integral Calculus (4h/4h)

Indefinite Integral

Definite Integral

Using definite integral for calculating area

Using definite integral for calculating rotation solids

Analytical Geometry (5h/5h)

Points and vectors in euclidean spaces

Basic vector operations

Straight lines in R^2

Straight lines and planes in R^3

Scalar product, vector product, normal vectors

Matrix Calculus (4h/4h)

Sum, difference, multiplication by scalar

Matrix multiplication

Determinant, inverse matrix

Matrix of rotation, matrix of reflection

Tutorial

Exercises directly related to the topics covered in lectures.

1. T. Garry, I. Wazir, K. Frederick, B. Landman, J. Nakamoto, J. Whalley, Mathematics Analysys and Approaches, Pearson 2019;

1. G.B. Thomas Jr, Thomas’s Calculus Revised Edition, Pearson 2014

2. R. Leitner, Zarys matematyki wyższej dla studentów cz. 1-3, PWN, Warszawa 2017

3. R. Leitner, W. Matuszewski, Z. Rojek, Zadania z matematyki wyższej cz. 1-2, PWN, Warszawa 2017

Material prepared by the lecturer.

Has knowledge in the field of Mathematics needed to solve project issues.

Has sufficient theoretical knowledge required to solve mathematical problems arising in simple engineering tasks.

Uses known mathematical rules to solve basic engeneering problems. Obtainins information from databases and other sources. Analyzing the outcomes of completed tasks.

Analyses basic physical and technical issues.

Uses mathematical models to carry out calculations.

Is open to the idea of self-education. Understands the need of improving profesional competences.

Understands the importance of his cousework.

60% - Exam

20% - Homework

20% - Engagement