- Application of mathematics in the solution of engineering problems
- Formulation of mathematical models for the solution of engineering problems
In the end of the class the students should be able to:
- Find general and particular solutions of first order differential equations.
- Solve second order linear differential equations with constant coefficients
- Use the method of power series for the solution of linear differential equations
- Find and use appropriately the solutions of the Bessel and Legendre differential equations.
- Use the Laplace transform and its inverse for the solution of ordinary differential equations
- Solve linear systems of ordinary differential equations with constant coefficients
- Investigate the qualitative behavior of the solution of a non-linear differential equation without solving it
Ordinary differential equations (ODEs) basic concept and ideas. First order ODEs. Separable ODEs. Exact ODEs. Linear ODEs and Bernoulli equation. Homogeneous ODEs. Special form first order ODEs. Integrating factors. Linear second order ODEs. Homogeneous linear second order equations. Second order homogeneous ODEs with constant coefficients.
Non-homogeneous equations. Solution by undetermined coefficients. Solution by variation of parameters. Power series solution of differential equations. Legendre’s equation. Frobenious method. Bessel’s equation and functions. Laplace transforms and their properties. Transforms of step and delta functions. Solution of ODEs by Laplace transform. Systems of ODEs. Transformation of higher order ODEs to a system of first order ODEs. Linear systems and the Wronski determinant. Homogeneous systems with constant coefficients. Graphical representation of solutions and the phase plane. Critical points and their stability. Qualitative solution of nonlinear systems of ODEs.
LECTURES: 3 h/w
RECITATION: 2 h/w
Total Module Workload (ECTS Standards):
The results of the final written and/or oral examination are multiplied by a factor based on the performance of the student in the written tests given during the semester.
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