310-2211/03 – Mathematics I (M I)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 7 |
| Subject guarantor | Mgr. Petr Otipka, Ph.D. | Subject version guarantor | RNDr. Jan Kotůlek, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2023/2024 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithmus and methods. Students should learn how to
analyze problem,suggest a method of solution, analyze correctness of achieved results with respect to given conditions.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Differential calculus of function of one real independent variable: function of one variable, elementary functions, limit and continuity of a function, differentiation, extreme values of function, point of inflection, convex and concave function, L’Hospital’s rule.
Linear algebra: determinants, matrices, systems of linear equations.
Analytic geometry of the 3-dimensional space.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-pass the written three tests, 3 points (max 10) from each
-pass the test of the derivatives, 4 points (max 5)
Point classification: 15-35 points.
Exam
Practical part of an exam is classified by 0 - 55 points. Practical part is successful if student obtains at least 20 points.
Theoretical part of the exam is classified by 0 - 10 points. Theoretical part is successful if student 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
E-learning
http://lms.vsb.cz
Other requirements
No special requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1 Functions of one real variable (definitions and basic properties)
2 Elementary functions
3 Limit of the function, continuity of the functions , basic rules
4 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation)
5 Derivatives of selected functions
6 Differential of the function, parametric differentiation, highes-order derivative
7 Applications of the derivatives
8 Monotonic functions and extremes of function, convexity and concavity of a function
9 Linear algebra: Matrice (basic properties), determinants (basic properties, calculation, evaluation)
10 Matrix inversion
11 Systems of linear equations, Cramer’s rule
12 Gaussian elimination
13 Product of vectors (basic properties). Analytical geometry in E3
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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