Ordinary Differential Equations. Practical Work
Author(s):
Andrei V. Panteleev
Moscow aviation institute (national research university),
Mathematical cybernetics department, head of department
Doctor of physico-mathematical sciences
avpanteleev@inbox.ru
Albina S. Yakimova
Moscow aviation institute (national research university),
Mathematical cybernetics department, associate professor
as.yakimova@yandex.ru
Konstantin A. Rybakov
Moscow aviation institute (national research university),
Mathematical cybernetics department, associate professor
Candidate of physico-mathematical sciences
rkoffice@mail.ru
Abstract:
Analytical, approximate and numerical methods and
algorithms for ordinary differential equations are described.
The using of each method is demonstrated for typical and non-typical examples
covering various applications for mechanics, economics, electrical circuits and
biological systems. Particular attention is paid to the analysis and stability
problems for one-dimensional and multi-dimensional dynamical systems.
The textbook is written according to last requirements of Federal state
educational standard. This textbook is recommended for students
in natural sciences, engineering and technology, computer science
and economics (for bachelor and master degrees).
Keywords
- analysis of output processes
- analytical method
- approximate method
- differential equations
- dynamical systems
- Laplace transform
- numerical method
- spectral method
- stability
- systems of differential equations
References:
- Panteleev A. V., Yakimova A. S., Rybakov K. A. Obyknovennye differentsial'nye uravneniya. Praktikum [Ordinary differential equations. Practical work]. Moscow, Infra-M, 2016
- Bortakovskiy A. S., Panteleev A. V. Lineynaya algebra v primerakh i zadachakh [Linear algebra: Examples and problems]. Moscow, Infra-M, 2015
- Bortakovskiy A. S., Panteleev A. V. Analiticheskaya geometriya v primerakh i zadachakh [Analytic geometry: Examples and problems]. Moscow, Infra-M, 2016
- Bortakovskiy A. S., Panteleev A. V. Lineynaya algebra i analiticheskaya geometriya. Praktikum [Linear algebra and analytic geometry: Practical work]. Moscow, Infra-M, 2015
- Panteleev A. V., Bortakovskiy A. S. Teoriya upravleniya v primerakh i zadachakh [The control theory: Examples and problems]. Moscow, Infra-M, 2016
- Panteleev A. V., Kudryavtseva I. A. Chislennye metody. Praktikum [Numerical methods: Practical work]. Moscow, Infra-M, 2017
- Panteleev A. V., Yakimova A. S., Rybakov K. A. Obyknovennye differentsial'nye uravneniya. Prakticheskiy kurs [Ordinary differential equations. Practical course]. Moscow, Logos, 2010
