XADIC Differential and Integral Calculus

Moravská vysoká škola Olomouc
léto 2022
Rozsah
3/2/0. 6 kr. Ukončení: zk.
Vyučující
doc. RNDr. Martina Pavlačková, Ph.D. (přednášející)
Garance
doc. RNDr. Martina Pavlačková, Ph.D.
Moravská vysoká škola Olomouc
Dodavatelské pracoviště: Moravská vysoká škola Olomouc
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
The objective of the course is to familiarise students with differential and integral calculus of functions of one and more variables and their applications. After completing the course, students understand the concept of function and they are aware of the utility of functions for description of relations between individual variables, they are also able to recognise and characterise the basic properties of functions. For functions of one or more variables they determine the domains of functions with certainty, define the limit of a function, know the properties of limits and are able to calculate the limits of various functions as well as understand the concept of function continuity. They understand and are able to define a derivative of a function, they routinely manage the calculation of derivatives of various functions and understand the geometric meaning of a derivative. They are able to use all their knowledge of differential calculus. They are able to define a primitive function and an indefinite integral for the function of one variable and they master the basic integration methods. For functions of one or more variables they understand the way a definite integral is constructed, and they have knowledge of its basic properties and calculation. They are able to apply the knowledge of integral calculus in order to solve basic geometric and physical problems.
Osnova
  • 1. Functions of one variable. (Function properties. Elementary functions and inverse functions. Logarithmic functions and exponential functions. Cyclometric functions.)
  • 2. Limit of a function. Continuity of a function. (Definition of the limit of a function. Rules for calculating limit of a function. Definition of continuity. Types of discontinuity.)
  • 3. Derivative of a function. (Definition of the derivative of a function and its geometric meaning. Rules for calculating derivative. Difference and differential of a function.)
  • 4. Application of differential calculus (L'Hôpital’s rule, investigation of the function course.)
  • 5. Indefinite integrals. (The concept of primitive function. Formulas for integration of elementary functions. The substitution method, integration by parts.)
  • 6. Definite integrals. (Definition of the Riemann’s definite integral. Newton-Leibniz theorem for calculating a definite integral. The substitution method and integration by parts applied on a definite integral.)
  • 7. Improper integrals. (Improper integral of Type 1. Improper integral of Type 2.)
  • 8. Application of integrals. (Geometric applications of definite and improper integrals.)
  • 9. Multivariable functions. (Basic definition, the limit and continuity.)
  • 10. Partial derivatives and total differentials. (Definition, rules for differentiation, the use of total differentials.)
  • 11. Extrema of Multivariable Functions. (Local and global extrema.)
  • 12. Implicit functions. (Definition, derivatives and constrained extrema.)
Literatura
    povinná literatura
  • HAEUSSLER, E. F., R. S. PAUL a R. J. WOOD. Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences. 14th ed. Pearson Canada, 2018, 848 s. ISBN 978-0-13-414110-7. info
  • DOWLING, E T. Schaum's Outline of Mathematical Methods for Business and Economics (Schaum's Outline Series). 1st ed. New York: N.Y.: McGraw-Hill, 2009. ISBN 978-0-07-163532-5. info
    doporučená literatura
  • CHIANG, A. a K. WAINWRIGHT. Fundamental methods of mathematical economics. 4th edition. New York: McGraw-Hill, 2005. info
  • JACQUES, I. Mathematics for economics and business. 9th edition. Pearson, 2018. info
Metody hodnocení
Course credit: active participation in seminars, credit assignment. Examination: written examination, (min. 50%), oral examination (min. 50%).
Vyučovací jazyk
Angličtina
Další komentáře
Předmět je vyučován každoročně.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích léto 2024.