ECE3040 Chapter 2.pdf - Chapter 2 The lecture notes are selected from the public Powerpoint lecture documents provided by Authors Autar Kaw Sri Harsha

ECE3040 Chapter 2.pdf - Chapter 2 The lecture notes are...

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Chapter 2 The lecture notes are selected from the public Powerpoint lecture documents provided by Authors: Autar Kaw, Sri Harsha Garapati
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Differentiation Continuous Functions
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Forward Difference Approximation     x x f x x f x x f Δ Δ 0 Δ lim For a finite ' Δ ' x     x x f x x f x f
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x x+ Δ x f(x) Figure 1 Graphical Representation of forward difference approximation of first derivative. Graphical Representation Of Forward Difference Approximation
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Example 1 The velocity of a rocket is given by   30 0 , 8 . 9 2100 10 14 10 14 ln 2000 4 4 t t t t where ' ' ν is given in m/s and ' ' t is given in seconds. a) Use forward difference approximation of the first derivative of to calculate the acceleration at . Use a step size of . b) Find the exact value of the acceleration of the rocket. c) Calculate the absolute relative true error for part (b).   t ν s t 16 s t 2 Δ
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