310-2117/03 – Mathematics 1 (M1)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |
| Subject guarantor | RNDr. Jan Kotůlek, 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 | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is an essential part of the engineering programmes. Nevertheless, it is not a a goal on its own, but rather a necessary tool for understanding the technical subjects.
Therefore, we aim to both introducing the basic mathematical concepts and deepen the logical and analytical thinking of our students.
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 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 and oral exam.
E-learning
http://mdg.vsb.cz/portal/
Other requirements
The exam consists of the following three parts: Computation of the derivatives of elementary functions (5 tasks, 15 minutes), the practical part (6 problems, 60 minutes, maximum 60 points) and the theoretical test with 10 questions (correct answer 2 points, no answer 0 points, wrong answer -1 point).
A student has to compute correctly 3 derivatives, obtain at least 25 points at the practical part and at least 5 points at the theoretical test.
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. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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