CHE110-L04 - Numerical Differentiation & Integration CHE110...

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Department of Chemical Engineering Numerical Differentiation & Integration CHE110 Introduction to Programming & Problem Solving
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Department of Chemical Engineering Numerical Derivatives Numerical derivatives are required when we need to know the rate of change of a quantity whose values are only known at discrete points ( e.g. experimental measurements). Example: Evaporation of Liquid time (min) liquid mass (g) 0 12.3 1 10.7 29 . 5 38 . 6 47 . 8 57 . 1 66 . 5 76 . 0 85 . 6 What is the evaporation rate?
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Department of Chemical Engineering Numerical Derivatives i1 i i i yy dy dx x x + + ⎛⎞ ⎜⎟ ⎝⎠ Forward Difference: ii 1 1 i dy dx x x Backward Difference: i dy dx x x + + Central Difference: i-1 i i+1 i-1 i i+1 i-1 i i+1
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Department of Chemical Engineering Numerical Integration Numerical integration is required when we need to know the integral of a quantity where the integrand is only known at discrete points
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This note was uploaded on 03/08/2009 for the course CHE 101 taught by Professor Coronel during the Spring '06 term at Rose-Hulman.

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CHE110-L04 - Numerical Differentiation & Integration CHE110...

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