Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |

Subject guarantor | RNDr. Petr Volný, Ph.D. | Subject version guarantor | RNDr. Petr Volný, Ph.D. |

Study level | undergraduate or graduate | ||

Study language | English | ||

Year of introduction | 2019/2020 | Year of cancellation | 2019/2020 |

Intended for the faculties | FAST | Intended for study types | Bachelor |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

DUB02 | RNDr. Viktor Dubovský, Ph.D. | ||

JAR71 | Mgr. Marcela Jarošová | ||

KRC23 | Mgr. Jitka Krčková, Ph.D. | ||

PAL39 | RNDr. Radomír Paláček, Ph.D. | ||

STA50 | RNDr. Jana Staňková, Ph.D. | ||

VOL06 | RNDr. Petr Volný, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 3+3 |

Goals and competence
Mathematics is an 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
analyse problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyse 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.

Lectures

Individual consultations

Tutorials

Other activities

Mathematics I is connected with secondary school education. It is divided in three parts, differential calculus of functions of one real variable, linear algebra and analytic geometry in the three dimensional Euclidean space E3. The aim of the first chapter is to handle the concept of a function and its properties, a limit of functions, a derivative of functions and its application. The second chapter emphasizes the systems of linear equations and the methods of their solution. The third chapter introduces the basics of vector calculus and basic linear objects in three dimensional space.

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3, http://mdg.vsb.cz/portal/en/Mathematics1.pdf.
Trench, W.F.: Introduction to real analysis, Free Edition 1.06, January 2011, ISBN 0-13-045786-8.

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.

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 50 - 0
National grading scheme excellent very good satisfactory failed
List of theoretical questions
1. Definition of real functions of one real variable
2. Monotonic functions
3. Bounded functions
4. Even, odd and periodic functions
5. Composite functions
6. One-to-one functions, inverse functions
7. Trigonometric functions, D(f), H(f), graph
8. Inverse trigonometric functions, D(f), H(f), graph
9. Limit of a function
10. One-side limit
11. Limit theorems
12. Continuity of functions
13. Definition of derivation of function at a point
14. Geometrical meaning of derivation of function at a point
15. Derivation rules
16. Derivation of composite functions
17. Derivation of function f(x)^g(x)
18. Derivation of parametric and implicit functions
19. Differential of functions
20. Taylor polynomial
21. l´Hospital rule
22. Extrema of functions
23. Concavity, convexity, inflection points
24. Asymptotes
25. Matrices
26. Matrices, algebraic operations
27. Rank of a matrix
28. Determinant of a matrix
29. Inverse
30. System of linear equations
31. Frobenius theorem
32. Cramer´s rule
33. Gaussian elimination algorithm
34. Scalar and triple product of vectors
35. Cross product of vectors
36. Equation of a line in a 3-dimensional space
37. Equation of a plane in a 3-dimensional space
38. Relative position of two lines
39. Relative position of a line and plane
40. Relative position of two planes
41. Distance of a point from a line
42. Distance of a point from a plane
43. Angle between lines
44. Angle between a line and a plane
45. Transversal and common perpendicular of two skew lines

http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)

There are not another requirements.

Subject has no prerequisities.

Subject has no co-requisities.

Syllabus of lecture
1. Real functions of one real variable. Definition, graph. Bounded function, monotonic functions, even, odd and periodic functions. One-to-one functions, inverse and composite functions.
2. Elementary functions (including inverse trigonometric functions).
3. Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
4. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules.
5. Derivative of elementary functions.
6. Differential of a function. Derivative of higher orders. l’Hospital rule.
7. Relation between derivative and monotonicity, convexity and concavity of a function.
8. Extrema of a function. Asymptotes. Plot graph of a function.
9. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
10. Determinants, properties of a determinant.
11. Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
12. Analytic geometry. Euclidean space. Scalar, cross and triple product of vectors, properties.
13. Equation of a plane, line in E3. Relative position problems.
14. Metric or distance problems.
Syllabus of tutorial
1. Domain of a real function of one real variable.
2. Bounded function, monotonic functions, even, odd and periodic functions.
3. One-to-one functions, inverse and composite functions. Elementary functions.
4. Inverse trigonometric functions. Limit of functions.
5. Derivative and differential of functions.
6. l’Hospital rule. Monotonic functions, extrema of functions.
7. 1st test (properties of functions, limits). Concave up function, concave down function, inflection point.
8. Asymptotes. Course of a function.
9. 2nd test (derivative of a function). Matrix operations.
10. Elementary row operations, rank of a matrix, inverse.
11. Determinants.
12. Solution of systems of linear equations. Gaussian elimination algorithm.
13. 3rd test (linear algebra). Analytic geometry.
14. Reserve.

Conditions for completion are defined only for particular subject version and form of study

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