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Calculus 2 - NMMA122

Title:	Kalkulus 1
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	summer
E-Credits:	10
Hours per week, examination:	summer s.:4/4, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Additional information:	https://matematika.cuni.cz/pyrih-kalkulus.html

Guarantor:	doc. RNDr. Pavel Pyrih, CSc.
Teacher(s):	RNDr. Kristýna Kuncová, Ph.D. doc. RNDr. Bohumír Opic, DrSc. doc. RNDr. Pavel Pyrih, CSc.
Class:	M Bc. FM M Bc. FM > Povinné M Bc. FM > 1. ročník
Classification:	Mathematics > Real and Complex Analysis
Co-requisite :	NMMA111
Incompatibility :	NMAA072
Interchangeability :	NMAA072
Is incompatible with:	NMMA112
Is interchangeable with:	NMMA112
In complex pre-requisite:	NMFM204, NMFM205, NMMA211, NMMA212, NMMA221, NMNM211, NMSA336

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

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)

Course completion requirements -

CONDITIONS FOR SEMESTER 2024/25

Conditions for granting credit

participation in lectures and exercises

(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)

successfully passed three credit tests

(the last week of classes, or during the deadlines in SIS, it is possible to retake the missing tests)

recording a video presentation of two topics from calculus

..................................................

Conditions for passing the exam

credit awarded

successful passing of the theory test

successful passing of the practice test

However, in justified cases (especially during the second revision period), the exam can be conducted orally (answering questions), or in a combination of oral and written form.

Detailed information is in the individual files at the address

https://matematika.cuni.cz/pyrih-kalkulus.html

Last update: Pyrih Pavel, doc. RNDr., CSc. (11.02.2025)

Literature -

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)

Teaching methods -

see https://matematika.cuni.cz/pyrih-kalkulus.html

Last update: Pyrih Pavel, doc. RNDr., CSc. (27.01.2025)

Requirements to the exam -

see Course completion requirements

Last update: Cúth Marek, doc. Mgr., Ph.D. (17.02.2024)

Syllabus -

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

3. Definite integral

(a) Newton's integral (calculation methods, substitutions, per partes)

(b) Riemann integral (definition, relation between Newton's and Riemann integral)

(d) Applications of definite integral

(e) Riemann-Stieltjes integral (definition, relation between Riemann-Riemann-Stieltjes integral)

4. Functions of several variables I

(a) basic concepts in R ^ n (closed and open sets, continuity)

(b) partial derivatives

5. Functions of several variables II

(a) implicit function theorem

(b) free and bounded extrema

Last update: Pyrih Pavel, doc. RNDr., CSc. (10.03.2025)

Entry requirements -

Understanding the material discussed in the lecture Mathematical Analysis I - NMTM101.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.02.2023)