SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Calculus II - OB2310N004
Title in English: Matematická analýza II
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: summer
E-Credits: 4
Examination process: summer s.:
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Is provided by: OPBM2M111A
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Mgr. Derek Pilous, Ph.D.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Pre-requisite : OB2310006
Interchangeability : OB2310004
Is pre-requisite for: OB2310N005, OB2310N217, OB1310206
Is interchangeable with: OKB2310N04
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)
The aim of the course is to introduce the students to the basic notions of the differential calculus (the notions of limit, continuity, derivative), to lead them to a deeper understanding of limit transition as a tool suitable to deal with real dynamical processes and to train them in practical calculations with limits and derivatives. Special attention will be given to the use of the notions and techniques of differential calculus in the study of elementary functions and in the physical applications.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)

To acquaint students with basic notions of calculus, lead them to understanding the relations between them, and teach them how to use theoretical knowledge for solving concrete problems

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)

Ross, K.A.:Elementary Analysis: The Theory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980

Fischer, E.: Intermediate Real Analisis. 1983

Lang, Serge: Undergraduate Analysis. Undergraduate Texts in Mathematics, Springer Verlag New York - Berlin - Heidelberg - Tokyo 1983

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)

The course includes lectures and seminars.

Requirements to the exam -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)

Seminar:

  • regular attendance
  • correct elaboration of homeworks
  • passing the current tests

Exam:

  • mastering of definitions, theorems and proofs, ability to illustrate them by examples and counterexamples
  • mastering of methods of calculation of primitive functions and integrals and ability to apply them to solving of problems
Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (07.06.2012)

Main topics:

  • The notion of the limit of a function (proper, improper, at a real point and at infinity), its calculation, "undetermined" expressions
  • Continuity of a function at a point and on an interval, properties of continuous functions, the relation of the notions continuity and limit
  • Derivative, its physical and geometrical interpretation, its calculation (especially for compound and inverse function), mean value theorems, l'Hospital rule.

The meaning of higher order derivatives for the behaviour of a function and the shape of its graph.

 
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