310-2111/04 – Mathematics I (MI)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | RNDr. Jan Kotůlek, Ph.D. | Subject version guarantor | RNDr. Jan Kotůlek, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | 2020/2021 |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to
- analyze problems,
- distinguish between important and unimportant,
- suggest a method of solution,
- verify each step of a method,
- generalize achieved results,
- analyze correctness of achieved results with respect to given conditions,
- apply these methods while solving technical problems,
- understand that mathematical methods and theoretical advancements
- outreach the field mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
The subject is divided into four chapters.
In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications.
In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Written test and both practical and theoretical exam
E-learning
http://mdg.vsb.cz/portal
Other requirements
There are no other requierements.
Prerequisities
Co-requisities
Subject syllabus:
Syllabus of lectures
I. Functions of one real variable
Definitions and basic properties, elementary functions, limit of the function, continuity of the functions, basic rules
II. Differential calculus functions of one real variable
The derivative of function (basic rules for differentiation), derivatives of selected functions, differential of the function, parametric differentiation, highes-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function
III. Linear algebra and analytical geometry
Matrice (basic properties), determinants (basic properties, calculation, evaluation), matrix inversion, systems of linear equations, Cramer’s rule, Gaussian elimination, product of vectors (basic properties), analytical geometry in E3
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction