Lecturer(s)


Knobloch Roman, Mgr. Ph.D.

Finěk Václav, doc. RNDr. Ph.D.

Bittnerová Daniela, RNDr. CSc.

Břehovský Jiří, Mgr. Ph.D.

Bittner Václav, Mgr. Ph.D.

Course content

Lectures: 1. Sets, numbers, inequality, supremum and infimum, logic, proofs in mathematics, functions. 2. Compositions of functions, inverse functions, mathematical functions and their properties, plane curve. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Derivatives and differentials. 6. Repetition. 7. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 8. Monotone functions, convex and concave functions, meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. 9. Riemann integral. 10. Primitive integral, integration by parts and by substitution, the fundamental theorems of integral calculus. 11. Integration of rational and some irrrational functions. 12. Integration of rational and some irrrational functions. 13. Geometric applications of Riemann integral, basic numerical methods for nonlinear equations and basic numerical quadratures. 14. Repetition. Practice: 1. Sets, numbers, inequality, supremum and infimum, logic, proofs in mathematics, functions. 2. Compositions of functions, inverse functions, mathematical functions and their properties, plane curve. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Derivatives and differentials. 6. Repetition. 7. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 8. Monotone functions, convex and concave functions, meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. 9. Investigation of functions. 10. Riemann and primitive integral, integration by parts and by substitution, the fundamental theorems of integral calculus. 11. Integration of rational and some irrrational functions. 12. Integration of rational and some irrrational functions. 13. Geometric applications of Riemann integral, basic numerical methods for nonlinear equations and basic numerical quadratures. 14. Repetition.

Learning activities and teaching methods

Monological explanation (lecture, presentation,briefing)
 Class attendance
 70 hours per semester
 Preparation for credit
 28 hours per semester
 Preparation for exam
 42 hours per semester
 Home preparation for classes
 40 hours per semester

Learning outcomes

The subject represents an introduction to calculus (differential and integral) of function of one real variable.
Calculus (differential and integral) of function of one real variable.

Prerequisites

Knowledge of secondary school mathematics.

Assessment methods and criteria

Combined examination
Credit: Active participation on seminars + tests. Exam: writtten.

Recommended literature


Brabec, J.  Martan, F.  Rozenský, Z.:. Matematická analýza I. Praha, SNTL, 1985.

Budinský, B.  Charvát, J.:. Matematika I [skriptum ČVUT fakulta stavební]. Praha, 2000.

Mezník, I.  Karásek, J.  Miklíček, J. Matematika 1 pro strojní fakulty. Praha, SNTL, 1992.

Nekvinda, M.  Vild, J.:. Matematické oříšky I. Liberec, 2000. ISBN 8070837624.

Nekvinda, M.  Vild, J.:. Náměty pro samostatné referáty z matematiky. Liberec, 1995.

Nekvinda M.:. Matematika I [Skriptum TUL]. Liberec, 1999.

Rektorys, K. a další. Přehled užité matematiky. Praha, 1995.
