310-2301/01 – Mathematics 1 (Math 1)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | RNDr. Jan Kotůlek, Ph.D. | Subject version guarantor | RNDr. Jan Kotůlek, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI, FMT, FBI, FS, HGF, FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
After completing this course, students should have the following skills:
* Use rules of differentiation to differentiate functions.
* Sketch the graph of a function using asymptotes, critical points.
* Apply differentiation to solve problems.
* Solve a system of linear algebraic equations.
* Work with basic objects in three dimensional Euclidean space.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
I. Calculus.
Function of one variable (basic notions, inverse function, elementary functions);
Limits and Continuity of a function;
Differentiation of a function (differentiation rules, application, L'Hospital's rule).
II. Linear algebra.
Vector spaces;
Matrices and determinants;
Systems of linear algebraic equations (Gaussian elimination, Frobeniu theorem).
III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 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://www.studopory.vsb.cz (in Czech)
Other requirements
There is no further requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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