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.
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