KMU255Programming_2ndClass_IntroMatModelingComputing

KMU255Programming_2ndClass_IntroMatModelingComputing -...

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Basis for Computing, Programming and Mathematical Modeling Selis Önel, PhD
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Programming writing instructions, that will make the computer follow and run a program based on those instructions Engineers use programming to solve numerical problems that come up as a result of mathematical modeling SelisÖnel© 2
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Numerical Analysis 1. Roots of equations 2. Systems of linear algebraic equations 3. Optimization 4. Curve fitting 5. Integration 6. Ordinary differential equations 7. Partial differential equations SelisÖnel© 3
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1. Roots of Equations Solve f(x) = 0 for x SelisÖnel© 4
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2. Linear Algebraic Equations Given a 11 , a 12 , a 21 , a 22 and y 1 , y 2 as constant parameters, solve for x’s a 11 x 1 + a 12 x 2 = y 1 a 21 x 1 + a 22 x 2 = y 2 SelisÖnel© 5
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3. Optimization Determine x that gives minimum (or maximum) f(x) SelisÖnel© 6
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4. Curve Fitting Fit a function (or functions) to a set of data SelisÖnel© 7
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5. Integration Find the area I under the curve SelisÖnel© 8 1 () ( , ) ( , ) b a i i i i I f x dx dy y f t y dt t y y f t y t  a b
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6. Ordinary Differential Equations Given Solve for y as a function of t SelisÖnel© 9 22 ( , ) ( , ) dy y f t y dt t uu f x y dx dy   1 ( , ) i i i i y y f t y t 
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7. Partial Differential Equations Given Solve for u as a function of x and y SelisÖnel© 10 22 ( , ) uu f x y dx dy  
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SelisÖnel© 11 Mathematical Modeling and Numerical Analysis Mathematical model uses mathematical language to describe a system Application fields: - Natural sciences and engineering disciplines - Physics, biology, earth science, meteorology, electrical engineering, chemical engineering, mechanical engineering, … - Social sciences - Economics, psychology, sociology, political science,
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SelisÖnel© 12 Mathematical Modeling and Numerical Analysis Eykhoff”s definition of Mathematical model (1974) ‘A representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'. Mathematical models can take many forms: (including but not limited to) dynamical systems, statistical models, differential equations, game theoretic models.
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This note was uploaded on 03/14/2012 for the course CHEMICAL E kmu 255 taught by Professor Onel,selis during the Fall '11 term at Hacettepe Üniversitesi.

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KMU255Programming_2ndClass_IntroMatModelingComputing -...

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