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# 01 - 1 Mathematical Modelling Numerical Methods and Problem...

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1: Mathematical Modelling Numerical Methods and Problem Solving ECOR2606 - Hassan & Holtz 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. Illustrate the conservation laws that form the basis of mathematical models in engineering. Introduce the different types of numerical methods that we will study in this course. ECOR2606 - Hassan & Holtz 3 A Simple Mathematical Model Wish to predict velocity as a function of time. In general: functions forcing parameters variables t independen variable Dependent , , f =

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ECOR2606 - Hassan & Holtz 4 A Simple Mathematical Model (contd.) Math. model of Newton's 2 nd law of motion: or, rewriting: Expressing acceleration as the time rate of change of velocity ( dv/dt ): ma = F m F = a m F = dt dv ECOR2606 - Hassan & Holtz 5 A Simple Mathematical Model (contd.) Downward force due to gravity: Upward force due to air resistance:
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01 - 1 Mathematical Modelling Numerical Methods and Problem...

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