Course: Mathematics

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Course title Mathematics
Course code AUM/L1LMT
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Cerman Zbyněk, Mgr. Ph.D.
  • Běták Vojtěch, Ing. Ph.D.
Course content
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.

Learning activities and teaching methods
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
prerequisite
Knowledge
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
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
Knowledge
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
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
Knowledge
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
Dialogic (Discussion, conversation, brainstorming)
Dialogic (Discussion, conversation, brainstorming)
Individual work of students
Individual work of students
Teamwork
Teamwork
Practice exercises
Practice exercises
assessment methods
Knowledge
Written examination
Written examination
Grade (Using a grade system)
Grade (Using a grade system)
Recommended literature
  • HOŠKOVÁ, Š., KUBEN, J., RAČKOVÁ, P. Integrální počet funkcí jedné proměnné. 2006.
  • KREML, P., VLČEK, J., VOLNÝ, P., KRČEK, J., POLÁČEK, J. Matematika II. ISBN 978-80-248-1316-5.
  • Matejdes M. Aplikovaná matematika. MAT-Centrum Zvolen, 2005.
  • Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné: vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
  • Pavlíková P., Schmidt O. Základy matematiky. Praha, 2006. ISBN 80-7080-615-X.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester