# Mathematical Modeling

May 9th, 2015
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• Recognize the difference between analytical and numerical solutions. • Recognize the distinction between truncation and round-off errors. • Understand the concepts of significant figures, accuracy, and precision. • Recognize the difference between true relative error t, approximate relative error a, and acceptable s error 10:51:09 PM

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Numerical AnalysisThe Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306Chapter 1Mathematical Modeling10:51:09 PMPart one : Approximation and ErrorsSpecific Study Objectives Recognize the difference between analytical and numerical solutions. Recognize the distinction between truncation and round-off errors. Understand the concepts of significant figures, accuracy, and precision. Recognize the difference between true relative error t, approximate relative error a, and acceptable s error 10:51:09 PMChapter 1: Mathematical ModelingMathematical Model A formulation or equation that expresses the essential features of a physical system or process in mathematical terms. Generally, it can be represented as a functional relationship of the form10:51:09 PMMathematical Modeling10:51:09 PMSimple Mathematical ModelExample: Newtons Second Law (The time rate of change of momentum of a body is equal to the resultant force acting on it) a = acceleration (m/s2) .the dependent variable m = mass of the object (kg) .the parameter representing a property of the system. f = force acting on the body (N)10:51:09 PMComplex Mathematical ModelExample: Newtons Second Law10:51:09 PMWhere: c = drag coefficient (kg/s), v = falling velocity (m/s)Complex Mathematical ModelAt rest: (v = 0 at t = 0), Calculus can be used to solve the equation10:51:09 PM

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