310-2111/01 – Mathematics I (MI)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | RNDr. Jan Kotůlek, Ph.D. | Subject version guarantor | Mgr. Monika Jahodová, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | 2022/2023 |
| 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
- participation on tutorials is obligatory, 20% of absence can be excused,
- submission of problem sheets,
- passing 10 written tests, maximally 2 points each.
Point classification: 5-20 points.
E-learning
http://mdg.vsb.cz/portal
http://www.studopory.vsb.cz
Other requirements
Exam:
Practical part of an exam is classified by 0 - 60 points. Student passes the practical part if (s)he obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Student passes the theoretical part if (s)he obtains at least 5 points.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
Prerequisities
Co-requisities
Subject syllabus:
Syllabus of lectures
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-Euclidean space.
14 Reserve.
Syllabus of tutorials
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-Euclidean space.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction