714-0665/02 – Mathematics I (M I)
| 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 | | |
| | Study language | Czech |
| Year of introduction | 2004/2005 | Year of cancellation | 2009/2010 |
| 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
Differential calculus of function of one real independent variable: functionof one variable, elementary functions limit and continuity of a function, differentiation, extreme values of function, point of inflection, convex and concave function, L’Hospital’s rule.
Linear algebra: determinants, matrices, systems of linear equations.
Analytic geometry of the 3-dimensional space.
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
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of lecture
1 Linear algebra: Matrice (basic properties), determinants (basic properties, calculation, evaluation)
2 Matrix inversion
3 Systems of linear equations, Cramer’s rule
4 Gaussian elimination
5 Product of vectors (basic properties)
6 Analytical geometry in E3
7 Functions of one real variable (definitions and basic properties)
8 Elementary functions
9 Limit of the function, continuity of the functions , basic rules
10 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation)
11 Derivatives of selected functions
12 Differential of the function, parametric differentiation, highes-order derivative
13 Applications of the derivatives
14 Monotonic functions and extremes of function, convexity and concavity of a function
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.