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The second part of a four-semester course in calculus for bachelor's program Financial Mathematics.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (30.05.2019)
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CONDITIONS FOR SEMESTER 2024/25
Conditions for granting credit
(missing participation in exercises can be replaced by counting 3 examples of appropriate quality that were not counted in the exercise after completing the notes... checked by the instructor; missing participation in a lecture can be replaced by carefully writing the sequence definition+theorem+proof+example for the missed material after completing the notes... checked by the instructor)
(the last week of classes, or during the deadlines in SIS, it is possible to retake the missing tests)
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Conditions for passing the exam
During the second retake, the exam will be supplemented by an oral exam, which can replace failed tests if the student has adequate knowledge.
Detailed information is in the individual files at the address
https://matematika.cuni.cz/pyrih-kalkulus.html Last update: Pyrih Pavel, doc. RNDr., CSc. (03.02.2025)
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O. Hájková, M. Johanis, O. John, O. Kalenda, M. Zelený: Matematika P. Holický, O. Kalenda: Metody řešení vybraných úloh z matematické analýzy pro 2. - 4. semestr V. Jarník: Integrální počet I, II V. Jarník: Diferenciální počet I, II Last update: Pyrih Pavel, doc. RNDr., CSc. (31.01.2021)
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see https://matematika.cuni.cz/pyrih-kalkulus.html Last update: Pyrih Pavel, doc. RNDr., CSc. (27.01.2025)
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see Course completion requirements Last update: Cúth Marek, doc. Mgr., Ph.D. (17.02.2024)
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1. Taylor polynomial (a) Basic properties (Taylor polynomial, Lagrange form of a residue). (b) Taylor polynomials of elementary functions
2. Primitive functions (a) Basic properties (arithmetic, substitution theorems, integration per partes) (b) Integration of rational functions (c) Some special substitutions
3. Definite integral (a) Newton's integral (calculation methods, substitutions, per partes) (b) Riemann integral (definition, relation between Newton's and Riemann integral) (c) Convergence of the Newton integral (comparison criterion) (d) Applications of definite integral (e) Riemann-Stieltjes integral (definition, relation between Riemann-Riemann-Stieltjes integral)
4. ODE (a) 1st order (Separated variables, homogeneous, kinear, applications) (b) 2nd order (Linear, constant coefficients)
5. Functions of several variables I (a) basic concepts in R ^ n (closed and open sets, continuity) (b) partial derivatives Last update: Pyrih Pavel, doc. RNDr., CSc. (04.02.2023)
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Understanding the material discussed in the lecture Mathematical Analysis I - NMTM101. Last update: Pyrih Pavel, doc. RNDr., CSc. (04.02.2023)
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