Ordinary and Partial Differential Equations

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Introductory course to the qualitative theory of ordinary and partial differential equations.

Requirements:

Syllabus of lectures:

Ordinary differential equations (ODE) and their systems: Linear systems, structure of the solution. Stability (by Lyapunov) of the solution of linear and nonlinear systems of ODE. Periodic solutions. Introduction to the theory of bifurcations. Solution of ODE by power series.

Partial differential equations (PDE): Surway and derivation of basic types of PDEs.

PDE of 1-st order - method of characteristics. Clasiffication of linear and Quasilinear PDEs of 2-nd order. The Fourier method of solution. Introduction to the modern theory of PDEs. Variational formulation of boundary value problems.

Syllabus of tutorials:

Ordinary differential equations (ODE) and their systems: Linear systems, structure of the solution. Stability (by Lyapunov) of the solution of linear and nonlinear systems of ODE. Periodic solutions. Introduction to the theory of bifurcations. Solution of ODE by power series.

Partial differential equations (PDE): Surway and derivation of basic types of PDEs.

PDE of 1-st order - method of characteristics. Clasiffication of linear and Quasilinear PDEs of 2-nd order. The Fourier method of solution. Introduction to the modern theory of PDEs. Variational formulation of boundary value problems.

Study Objective:

Introductory course to the qualitative theory of ordinary and partial differential equations.

Study materials:

1. Ferhulst, F., Nonlinear differential equations and dynamical systems, Springer, 2001, 2. Renardy, R.C., Rogers, J., An introduction to partial differential equations, Springer, 1993

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: