Mathematics 2

Course guarantor:

Tomáš Neustupa

Lecturer:

Tomáš Neustupa

Tutor:

Tomáš Neustupa

Supervisor:

Institute of Economic Studies

Synopsis:

Requirements:

Syllabus of lectures:

Calculus - functions of two or more variables

1) Taylors polynomial, Lagrange form of Remainder, applications.

2) Functions of more variables, domain, graph, isocurves.

3) Partial derivatives, gradient.

4) Tangent plane, total differential, directional derivative.

5) Local extremes of functions of two variables.

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

7) Constrained extremes, Lagrange multipliers.

Calculus - integration in 2D and 3D

8) Double integral, transformation to polar coordinates.

9) Triple integral, transformation to cylindrical coordinates.

Ordinary Differential Equations and its applications

10) Introduction to ordinary differential equations, separation of variable method.

11) Examples of applications of ODEs, non-separable ODEs, computation by approximation.

Syllabus of tutorials:

Calculus - functions of two or more variables

1) Taylors polynomial, Lagrange form of Remainder, applications.

2) Functions of more variables, domain, graph, isocurves.

3) Partial derivatives, gradient.

4) Tangent plane, total differential, directional derivative.

5) Local extremes of functions of two variables.

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

7) Constrained extremes, Lagrange multipliers.

Calculus - integration in 2D and 3D

8) Double integral, transformation to polar coordinates.

9) Triple integral, transformation to cylindrical coordinates.

Ordinary Differential Equations and its applications

10) Introduction to ordinary differential equations, separation of variable method.

11) Examples of applications of ODEs, non-separable ODEs, computation by approximation.

Study Objective:

Study materials:

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans: