Mathematics 2

Garant předmětu:

Lecturer:

Tutor:

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.

-Partial derivatives, gradient.

-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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Economics and Management 2019/20 (compulsory course)