CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Mathematics 2

Code Completion Credits Range Language
U63E1102 Z,ZK 6 2P+2C English
Garant předmětu:
Tomáš Neustupa
Lecturer:
Tomáš Neustupa, Jan Valášek
Tutor:
Tomáš Neustupa, Jan Valášek
Supervisor:
Institute of Economic Studies
Synopsis:

 Introduction to ordinary differential equations - order of equation,initial conditions, maximal solutions, classification of

equations, examples of applications

 Solutions to particular ODEs - the Fourier method, homogeneous equation of n-th order, non-homogeneous equation of n-th

order, the variation of constants formula, systems of linear first-order equations

 Series - definition, basic properties, convergence of series, convergence tests (the comparison test, the Cauchy test, the ratio

test), power series, the Taylor series

 Reccurence relations - solution to homogeneous and nonhomogeneous linear reccurence relations of an arbitrary order,

examples of applications

 Introduction to multidimensional calculus - functions with two dimensional domain, basic properties, their illustrations,

graphs and contour lines, introduction to their limits and continuity

 Derivative in multidimensional calculus - partial derivatives, differential, applications (local extremes, global extremes with

respect to sets, the Lagrange multipliers)

 Multidimensional integrations - measurable sets, the Fubini theorem, substitution, change of order of integration,

application in geometry and probability.

Requirements:
Syllabus of lectures:

Themes of lectures

-Taylor’s polynomial, Lagrange form of Remainder, applications.

-Functions of more variables, domain, graph, isocurves.

-Total differential, directional derivative.

-Local extremes of functions of two variables.

-Absolute (global) extremes of functions of two variables.

-Constrained extremes, Lagrange multipliers.

-Double integral, transformation to polar coordinates.

-Triple integral, transformation to cylindrical coordinates.

-Introduction to ordinary differential equations, separation of variable method.

-Examples of applications of ODE’s, non-separable ODE’s, computation by approximation.

Syllabus of tutorials:
Study Objective:
Study materials:

Neustupa J.: Mathematics II (textbook CTU).

Various Calculus books and lectures on internet.

Burda, P.: Mathematics III, Ordinary Differential Equations and Infinite Series, CTU Publishing House, Prague, 1998..

Herman, L.: Ordinary Differential Equations, CTU Publishing House

Note:
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomDEJ:M110Neustupa P.Valášek J.14:15–15:45(lecture parallel1)DejviceUčebnaroomDEJ:M110Neustupa P.Valášek J.16:00–17:30(parallel nr.101)DejviceUčebna
The course is a part of the following study plans:
Data valid to 2023-05-31
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