Lecturer(s)
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Cerman Zbyněk, Mgr. Ph.D.
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Běták Vojtěch, Ing. Ph.D.
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Course content
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Linear algebra: - Vector space, linear dependence and independence of vectors, basis. - Matrices, operations with matrices, rank. - Systems of linear equations, Gaussian elimination. Differential calculus: - Real function of one real variable, domain and codomain, graph, properties of the functions. - Algebraic and transcendental functions. - Limit of a function, theorems about limits, asymptote, continuity of a function. - Derivative of a function, enumeration of derivative, derivatives of higher orders. L'Hospital's rule. - Extrema of a function, intervals of monotonicity, convexity, concavity, inflex points. - Applications of the differential calculus in geometry, physics and economics. Integral calculus of the functions of one real variable: - Primitive function, indefinite integral, integration by parts, substitution rule. - Definite integral, definition, basic properties and enumeration of definite integral. - Applications of definite integral in geometry, physics and economics.
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Practice exercises
- Participation in classes
- 56 hours per semester
- Preparation for examination
- 45 hours per semester
- Home preparation for classes
- 4 hours per semester
- Preparation for course credit
- 20 hours per semester
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prerequisite |
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Knowledge |
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Have a basic understanding of high school mathematics |
Have a basic understanding of high school mathematics |
Have basic logical thinking |
Have basic logical thinking |
Read the materials provided and consult if there is any confusion |
Read the materials provided and consult if there is any confusion |
Skills |
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Show interest and effort in the subject |
Show interest and effort in the subject |
Regularly attend lectures and exercises |
Regularly attend lectures and exercises |
Be active in the exercises and answer questions during the lecture (every answer is appreciated) |
Be active in the exercises and answer questions during the lecture (every answer is appreciated) |
learning outcomes |
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Knowledge |
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Prohloubit logické myšlení |
Prohloubit logické myšlení |
Define and explain the basic concepts of mathematical analysis and linear algebra |
Define and explain the basic concepts of mathematical analysis and linear algebra |
Explain the concept of a real function of one real variable and the related concepts of definitional domain and value domain |
Explain the concept of a real function of one real variable and the related concepts of definitional domain and value domain |
List the basic elementary functions of one real variable, including their properties and graphs |
List the basic elementary functions of one real variable, including their properties and graphs |
Characterize the four basic types of limit functions of one real variable |
Characterize the four basic types of limit functions of one real variable |
Describe the geometric meaning of the derivative of a function at a point |
Describe the geometric meaning of the derivative of a function at a point |
Describe the procedure for investigating the progress of a function of one real variable |
Describe the procedure for investigating the progress of a function of one real variable |
Explain the concept of integral and distinguish between definite and indefinite integrals |
Explain the concept of integral and distinguish between definite and indefinite integrals |
Define a matrix over real numbers and describe matrix operations (sum, product, scalar multiplication, transpose). |
Define a matrix over real numbers and describe matrix operations (sum, product, scalar multiplication, transpose). |
Charakterizovat třídimenzionální vektorový prostor a popsat pojem báze prostoru. |
Charakterizovat třídimenzionální vektorový prostor a popsat pojem báze prostoru. |
Skills |
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Use active knowledge of the concept of functional value in calculations and sketches of graphs of functions |
Use active knowledge of the concept of functional value in calculations and sketches of graphs of functions |
Rozpoznat z grafu funkce intervaly, na kterých je funkce rostoucí, klesající, prostá, konvexní, konkávní |
Rozpoznat z grafu funkce intervaly, na kterých je funkce rostoucí, klesající, prostá, konvexní, konkávní |
Calculate limits using algebraic adjustments and L'Hospital's rule |
Calculate limits using algebraic adjustments and L'Hospital's rule |
Derive functions of one real variable using basic formulas and five rules for derivation. |
Derive functions of one real variable using basic formulas and five rules for derivation. |
Investigate the course of a function of one real variable (definition domain, limits, local extrema, inflections, asymptotes) |
Investigate the course of a function of one real variable (definition domain, limits, local extrema, inflections, asymptotes) |
Recognize the difference between the substitution method and the per-partes method for integrating a function of one real variable and apply it appropriately to a given type of example |
Recognize the difference between the substitution method and the per-partes method for integrating a function of one real variable and apply it appropriately to a given type of example |
Calculate the content of any figure bounded by curves |
Calculate the content of any figure bounded by curves |
Solve a system of linear equations with exactly one solution, using elementary row transformations. |
Solve a system of linear equations with exactly one solution, using elementary row transformations. |
Determine the linear dependence and independence of the vectors and, if necessary, the base of the space or subspace |
Determine the linear dependence and independence of the vectors and, if necessary, the base of the space or subspace |
teaching methods |
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Knowledge |
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Lecturing |
Lecturing |
Students working in pairs |
Students working in pairs |
Projection (static, dynamic) |
Projection (static, dynamic) |
Monologic (Exposition, lecture, briefing) |
Monologic (Exposition, lecture, briefing) |
Dialogic (Discussion, conversation, brainstorming) |
Dialogic (Discussion, conversation, brainstorming) |
Skills |
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Dialogic (Discussion, conversation, brainstorming) |
Dialogic (Discussion, conversation, brainstorming) |
Individual work of students |
Individual work of students |
Teamwork |
Teamwork |
Practice exercises |
Practice exercises |
assessment methods |
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Knowledge |
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Written examination |
Written examination |
Grade (Using a grade system) |
Grade (Using a grade system) |
Recommended literature
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HOŠKOVÁ, Š., KUBEN, J., RAČKOVÁ, P. Integrální počet funkcí jedné proměnné. 2006.
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KREML, P., VLČEK, J., VOLNÝ, P., KRČEK, J., POLÁČEK, J. Matematika II. ISBN 978-80-248-1316-5.
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Matejdes M. Aplikovaná matematika. MAT-Centrum Zvolen, 2005.
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Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné: vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
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Pavlíková P., Schmidt O. Základy matematiky. Praha, 2006. ISBN 80-7080-615-X.
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