Calculus 2 - NMMA122
Title: Kalkulus 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
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
Teaching methods: full-time
Additional information: https://www.karlin.mff.cuni.cz/~cuth/edu.php
Guarantor: doc. Mgr. Marek Cúth, Ph.D.
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
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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 2023/24

CREDIT Sufficient condition to gain a credit is 50% presence at exercises sessions and four successfully written credit exams. Credit exam "successfully written" if the student gets at least 7 points out of 20. In case the written credit exam is not successfully written it is possible to correct it by solving additional exercises (as many as is the number of missing points from the written credit exam). In those cases it is neccessary to contact teacher responsible for student's exercises session. Student asks for those additional exercises one week after obtaining the results from the written exam the latest.

EXAM The exam may be taken by those students who obtained a credit from Kalkulus 1. Exam has two parts - written and oral. In order to go to the oral exam, the student must pass through the written exam. If the student fails in the exam, s/he must pass through both parts (written and oral) again even if s/he has previously passed through the written exam.

WRITTEN PART OF THE EXAM Written exam will contain 4 computational exercises. Time to solve those is 120 minutes. Written exam is successfully written if the student gets 26 points out of 50. Student can use standard writing accessories and a self-made cheat sheat of the size of one page A4, no electronic devices are admitted to be used during the written exam.

ORAL PART OF THE EXAM During the oral part the student must formulate one definition and two Theorems/Propositions/Lemmata. Further, s/he must convince the examinator s/he understands the statement of those (typically one will be asked to show how concretely those results are used in his/her written exam). Next the student will be asked on one topic and s/he will shortly overview what was said about it during lectures - during this the student will be asked to show some proof(s). Neccessary condition to pass the exam is the knowledge of proofs.

Further details are described here: http://www.karlin.mff.cuni.cz/~cuth/Kalkulus1_pozadavky.pdf

Last update: Cúth Marek, doc. Mgr., Ph.D. (17.02.2024)
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://www.karlin.mff.cuni.cz/~cuth/edu.php

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

(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)
Entry requirements -

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

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