Ordinary Diferential Equations

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Department of Technical Mathematics

Synopsis:

Differential equation of first order, methods of solution, applications.

- Systems of equations of first order, linear systems, nonlinear systems, linearization.

- Stability of solution and Ljapunov functions.

- Fourier series and ODE.

- Basics of Laplace transformation and ODE.

- Matrix exponential.

- Diagonalization.

- Flow of the linear system and invariant spaces.

- Nonlinear systems.

- Hamilton, Newton and Gradient systems.

- Geomtetrical aspects of phase plane, periodic solutions.

- Dynamical systems and semigroups.

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Study materials:

Herrmann, L.: Infinite series & Ordinary differential equations. A concise survey with examples and solved exercises, 2014, Česká technika - nakladatelství ČVUT.

Perko, L.: Differential equations and dynamical systems. Third edition. Texts in applied mathematics 7, 2001, Springer-Verlag.

M.D.Greenberg: Ordinary Differential Equations

James C. Robinson: An Introduction to Ordinary Differential Equations

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: