Ordinary Differential Equations

Course guarantor:

Tomáš Neustupa

Lecturer:

Luděk Beneš, Tomáš Neustupa

Tutor:

Luděk Beneš, Tomáš Neustupa

Supervisor:

Department of Technical Mathematics

Synopsis:

The course expect the understanding of the subjects of previous study on „Alpha“ level.

Outline of concepts and technics of solving differential equations of first order. Autonomous systems. Geometrical aspects of phase plane. Stability of solution.

Requirements:

Syllabus of lectures:

• The overview of methods for solving ODE of the first order. Separation of variables, Bernouli's method, variation of parameters, integral factor method.

• Existence and uniqueness of the solution of the Cauchy problem.

• Specific applications of differential equations (move of a body, population models, changes in concentration of substances ...).

• Systems of differential equations. From equation of higher other to the system of equations of first order. Existence and uniqueness of solution. Properties of solution. Methods for solving (Euler's meth., var. of parameters).

• Stability of equilibrium solution of differential equation.

• Stability of linear and nonlinear systems. Criterion of stability. Attractors.

• Stability and linearization.

• Stability and Ljapunov functions.

• Extension to calculus (sequences of numbers, Cauchy sequence, sequences of functions, uniform convergence, linear space, scalar product, Hilbert space).

• Generalized Fourier's series. Bessel's inequality. Parceval's equality. Applications in differential equations.

• Basic introduction to Laplace transform and its use for differential equations.

Syllabus of tutorials:

Study Objective:

Study materials:

• Burda, P.: Mathematics III, Ordinary Differential Equations and Infinite Series, CTU Publishing House, Prague, 1998.

• W.A.Adkins, M.G.Davidson: Ordinary differential equations. 2004.

• Stanley J. Farlow: An introduction to differential equations and their applications. McGraw Hill, Inc., New York

• J.Polking, A.Boggess, D.Arnold: Differential Equations. Prentice Hall 2001

• R.K.Nagle, E.B.Saff: Fundamentals of Differential Equations and Boundary Value Problems. Addison W.Publ.Co.1993

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu	roomKN:D-105 Neustupa T. 09:00–10:30 (lecture parallel1) Karlovo nám. roomKN:D-105 Neustupa T. 10:45–11:30 (lecture parallel1 parallel nr.101) Karlovo nám.
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• 13 136 NSTI MMT 2012 základ (compulsory course in the program)