Course objectives
Define mathematical models in engineering practice. Apply mathematical models in typical engineering problems and solve them. Use of the appropriate methods for solving specific problems. Use of the specialized software packages.
Expected course learning outcomes
Recognize appropriate mathematical model for some physical problems. Differentiate models which are based on ordinary differential equations and models based on partial differential equations. Differentiate initial and boundary value problems. Formulate correctly appropriate mathematical model of physical problem. Explain correctly fundamental ideas and properties of different numerical approaches and methods for solving differential equations; explain correctly advantages and disadvantages of particular computational methods. Solve mathematical model with appropriate numerical method with the aid of existing or homemade software. Evaluate results of applied methods.
Course content
Introduction to mathematical modelling of technical systems. Models based on ordinary differential equations (ODE). Solving of initial problems and boundary value problems. Dynamical systems. Methods for solving dynamical systems. Models based on partial differential equations (PDE). Applications to viscous fluid flow, stationary heat transport, conservation laws, gas flow, shallow water.