714-0866/01 – 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 | 2009/2010 | Year of cancellation | 2019/2020 |
| Intended for the faculties | USP, FBI, FAST, HGF, FEI, FMT, FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
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, 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
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)
Other requirements
There is no further requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Program of lectures
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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:
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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.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.