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Course, academic year 2019/2020
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Calculus III seminar - OB1310201
Title in English: Matematická analýza III prohlubující seminář
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2010
Semester: winter
E-Credits: 1
Examination process: winter s.:
Hours per week, examination: winter s.:0/1 C [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
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: doc. RNDr. Jiří Jarník, CSc.
RNDr. František Mošna, Dr.
prof. RNDr. Ladislav Kvasz, DSc., Dr.
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
Co-requisite : OB2310005
Pre-requisite : OB2310004
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
Antiderivative, integral (Riemann, Newton), geometrical meaning, physical applications, elementary differential equations (especially linear equations).
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)

The purpose of the course is to make students acqiainted with concept of antiderivative - a basic concept of mathematical analysis, which represents important tool for calculation of several geometric, physic and other variables and for solutions of elementary (especially linear) differential equations.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
  • Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980
  • Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer Verlag NewYork-Heidelberg-Berlin 1983

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)

Lecture and seminar.

Requirements to the exam -
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
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 (11.03.2010)
  • Antiderivative, definition, properties, existence, basic formulas, methods (by parts, substitution, partial fraction decomposition)
  • Definite integral, Newton and Riemann integrals, Leibniz formula, methods of calculation, applications of integral in geometry (area, length of curve, solid of revolution volume and surface)
  • Differential equations , linear differential equations of the first order, linear differential equations of the second order with constant coefficients, equations with separated variables

 
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