Schedule WS 2016/2017
Mathematics I (NMMA711) - seminar
Old tests - Kalenda
Old tests - Zeleny
Exercises - Kalenda
Limits of a sequence
Limit of a function
Derivation of a function
Investigation of a function
Mathematics I (NMMA711) - course
Lecture texts: printout version, presentation.
A more detailed text.
Textbooks: book 1, book 2.
lecture 1 (26.10.2016) - introduction; basic notions of naive set theory; logic
lecture 2 (26.10.2016) - logic, predicates and quantifiers; methods of proofs and examples (de Morgan rules, Cauchy inequality)
lecture 3 (27.10.2016) - examples of proofs (Cauchy inequality, irrationality of the "square root of 2"); number sets, real numbers, the infimum axiom
lecture 4 (2.11.2016) - the infimum axiom, existence of a supremum, intervals, consequences of the infimum axiom - Archimedean property, existence of the integer part
lecture 5 (3.11.2016) - consequences of the infimum axiom - existence of the nth root, density of rational and irrational numbers
lecture 6 (3.11.2016) - sequences - definition, bounded and monotone sequences, examples, operations with sequences; limit of a sequence - definition, uniqueness, examples, boundedness of convergent sequences, limit of a subsequence
lecture 7 (9.11.2016) - limit of a sequence - limit arithmetics, product of a null and bounded sequences, limits and ordering, two policemen theorem
lecture 8 (9.11.2016) - infinite limits of sequences, extended real line, extended limit arithmetics, limit "one over 'positive' zero"
lecture 9 (10.11.2016) - infimum and supremum of unbounded sets, supremum and limits; limit of a monotone sequence
lecture 10 (26.11.2016) - Bolzano-Weierstrass theorem; mappings
lecture 11 (23.11.2016) - functions - basic definitions, limits, continuity, one-sided limits
lecture 12 (23.11.2016) - functions - one-sided continuity, local boundedness of function with a finite limit, arithmetics of limits and continuity
lecture 13 (24.11.2016) - functions - limit "one over 'positive' zero"; polynomials; limits and inequalities, product of a null and bounded function, limit of a compound function
lecture 14 (30.11.2016) - functions - Heine theorem, limit of a monotone function; functions continuous on an interval - continuity of a compound function, intermediate value theorem, an image of an interval under continuous function; definitions of extrema and local extrema
lecture 15 (1.12.2016) - functions continuous on an interval - Heine theorem for continuous functions, extrema of continuous functions on closed intervals, continuity of an inverse function; elementary functions - the logarithm
lecture 16 (1.12.2016) - elementary functions - the exponential function, trigonometric functions
lecture 17 (7.12.2016) - elementary functions - trigonometric functions, inverse trigonometric functions; derivative - definition, examples, tangent, continuity of a function with a finite derivative
lecture 18 (8.12.2016) - derivative - arithmetics of derivatives, derivative of a compound function, derivative of an inverse function
lecture 19 (14.12.2016) - derivatives of elementary functions; necessary condition for a local extremum, finding global extrema, Rolle and mean value theorems
lecture 20 (15.12.2016) - derivative and monotonicity, computation of the derivative as a limit of derivatives, l'Hospital's rule
lecture 21 (21.12.2016) - convex and concave functions, characterisation of convex functions; higher order derivatives, second derivative and convexity
lecture 22 (22.12.2016) - inflection point and its relation to second derivative; asymptotes at infinities; investigation of a function
Introductory Mathematics (NMMA713)
Introductory Mathematics exams 2014/2015, Information on exams for Introductory Mathematics
Několik užitečných rad a odpovědí na často kladené otázky.
Odpovědi na některé připomínky studentů IES ke kurzům matematiky.