714-0866/01 – Mathematics 1 (Math 1)
| Garantující katedra | Katedra matematiky a deskriptivní geometrie | Kredity | 5 |
| Garant předmětu | RNDr. Jan Kotůlek, Ph.D. | Garant verze předmětu | RNDr. Jan Kotůlek, Ph.D. |
| Úroveň studia | pregraduální nebo graduální | | |
| | Jazyk výuky | angličtina |
| Rok zavedení | 2009/2010 | Rok zrušení | 2019/2020 |
| Určeno pro fakulty | FBI, FEI, FS, FMT, HGF, USP, FAST | Určeno pro typy studia | bakalářské |
Cíle předmětu vyjádřené dosaženými dovednostmi a kompetencemi
Goals
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.
Vyučovací metody
Přednášky
Individuální konzultace
Cvičení (v učebně)
Anotace
Course description
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, Frobenius theorem).
III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).
Povinná literatura:
Doporučená literatura:
Další studijní materiály
Forma způsobu ověření studijních výsledků a další požadavky na studenta
Passing the course, requirements
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)
Další požadavky na studenta
Další požadavky na studenta nejsou.
Prerekvizity
Předmět nemá žádné prerekvizity.
Korekvizity
Předmět nemá žádné korekvizity.
Osnova předmětu
Program of lectures
--------------------------------------------------
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.
Program of exercises and seminars:
--------------------------------------------------
1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series.
2 Rank of matrix, inverse matrix.
3 Solution of linear equations.
4 Solution of systems of linear equations.
5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix).
6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions.
7 2.test (domain, inverse function). Limits of functions.
8 Differentiation of functions.
9 Derivations and differential, equations of tangents and normals point functions.
10 Calculation of the limit L'Hospital rule functions. Extremes of function.
11 Convex and concave function, inflection point.
12 3.test (derivative of the function, use). Asymptotes of the curve. A function.
13 Analytic geometry.
14 Reserve and credits.
Podmínky absolvování předmětu
Podmínky absolvování jsou definovány pouze pro konkrétní verzi předmětu a formu studia
Výskyt ve studijních plánech
Výskyt ve speciálních blocích
Hodnocení Výuky
Předmět neobsahuje žádné hodnocení.