MATHEMATICS II - LECTURES
doc. RNDr. Daniela Velichová, CSc.




Lecture 1 - Power series - radius and interval of convergence
Expansions of functions to Taylor and McLaurin series

Lecture 2 - Ordinary differential equations - basic concepts
ODE with separated and separable variables

Lecture 3 - Ordinary linear differential equations - order 1
Ordinary differential equations of order 2 - homogeneous

Lecture 4 - Non-homogeneous ordinary differential equations of order 2 with special right-hand members

Lecture 5 - Non-homogeneous ordinary difrerential equations of order 2 - variation of constants
Summary of ordinary difrerential equations

Lecture 6 - Euclidean space En
Introduction to vector algebra

Lecture 7 - Linear figures in the Euclidean space
Quadric surfaces

Lecture 8 - Functions in more variables - definition, domain, graph, limit and continuity

Lecture 9 - Partial derivatives and differential of functions in two variables

Lecture 10 - Local extrema of functions in two variables
Constrained and global extrema of functions in two variables

Lecture 11 - Multiple integrals
Double and triple integrals

Lecture 12 - Integral transformations

Lecture 13 - Applications of multiple integrals