01-Math Models, Num Methods, Prob Solving

01-Math Models, Num Methods, Prob Solving - 1: Mathematical...

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1: Mathematical Modelling 1: Mathematical Modelling Numerical Methods Numerical Methods and and Problem Solving Problem Solving
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September 20, 2006 13:17 2 Chapter Objectives Illustrate how mathematical models can be developed to model simple physical systems. Demonstrate how numerical methods can be used to generate solutions to mathematical models. show implementation on digital computers. Illustrate the conservation laws that form the basis of mathematical models in engineering. show differences between steady-state and dynamic solutions. Introduce the different types of numerical methods that we will study in this course.
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September 20, 2006 13:17 3 A Simple Mathematical Model Wish to predict velocity as a function of time. In general: Dependent variable : a characteristic that reflects behaviour. In our case: v (velocity). Independent variable : usually dimensions such as time and space, along which behaviour is determined. e.g.: t (time). Parameter : reflect system properties. e.g.: mass, drag coeff., etc. Forcing function : external influences. e.g.: gravitational attraction, wind resistance. Dependent variable = f independent variables , parameters , forcing functions
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September 20, 2006 13:17 4 A Simple Mathematical Model (contd.) Math. model of Newton's 2 nd law of motion:
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01-Math Models, Num Methods, Prob Solving - 1: Mathematical...

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