714-0660/01 – Basic Mathematics (ZM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 7 |
| Subject guarantor | Mgr. Jiří Vrbický, Ph.D. | Subject version guarantor | Mgr. Jiří Vrbický, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 1999/2000 | Year of cancellation | 2013/2014 |
| Intended for the faculties | FMT | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.
Students should learn how to
analyze problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyze correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements
outreach the field mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Linear Algebra: An algebraic vector, basic terms. A matrix, the rank of a
matrix, elementary treatments of a matrix. Systems of linear equations. A
determinant, determinant properties. Foundations of the matrix calculus.
The Real-Valued Function of a Real Variable: Definition, the domain of
definition, the range of values, the graph of a function. Properties of
functions. Inverse, composite functions. Basic elementary functions. The
sequence of real numbers and the limit of the sequence. The limit of a function
at a point. The continuity of a function.
The Derivation of a Function: Derivation definition and the geometric
significance of the derivation. The derivation of basic elementary functions.
Derivation Applications: A tangent and a normal. Monotony. Local and absolute
extreme values of a function. Convexity, concavity, inflection points.
Asymptotes. The behaviour of a function.
The Differential Calculus of Functions of Several Variables: The definition of
functions of two and several variables, the domain of definition. The partial
derivations of the first and higher orders.
The Indefinite Integral: An indefinite integral and a primitive function.
Basic formulas. Integration by parts. The method of substitution.
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
http://mdg.vsb.cz/M/
Other requirements
No special requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1 Linear algebra: Vectors, matrice (basic properties).
2 Determinants (basic properties, calculation, evaluation).
3 Matrix inversion.
4 Systems of linear equations, Cramer’s rule, Gaussian elimination.
5 Functions of one real variable (definitions and basic properties).
6 Elementary functions.
7 Limit of the function, continuity of the functions , basic rules.
8 Differential calculus functions of one real variable. The derivative of function (basic rules for differentiation).
9 Derivatives of selected functions.
10 Differential of the function, parametric differentiation, highes-order derivative.
11 Applications of the derivatives.
12 Monotonic functions and extremes of function, convexity and concavity of a function.
13 Integral calculus: antiderivative and indefinite integral for functions of one variable.
14 Integration methods - substitution, integration by parts.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction