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NUMERICALDIFFERENTIATIONANDINTEGRATION * Lecture series on “ Numerical Techniques and Programming in MATLAB” VBSPurvanchalUniversity, Jaunpur July 22-28, 2016 by Dr. Sarvesh Kumar, IIST Trivandrum Lecture series on “Numerical techniques and MATLAB”, July 22-28, 2016 Dr. Sarvesh Kumar, IIST Trivandrum. 1 Numerical Differentiation Basic problems • Derive a formula that approximates the derivative of a function in terms of linear combination of function values ( Function may be known) • Approximatethevalueofaderivativeofafunctiondefinedbydiscrete data. Lecture series on “Numerical techniques and MATLAB”, July 22-28, 2016 Dr. Sarvesh Kumar, IIST Trivandrum. 2 Solution Approaches .. • Use Taylor Series Expansion. • Pass a polynomial through the given data and differentiate the interpolating polynomial. Applications To solve Ordinary and Partial Differential Equations. Lecture series on “Numerical techniques and MATLAB”, July 22-28, 2016 Dr. Sarvesh Kumar, IIST Trivandrum. 3 First Derivative.. Let f : [a,b] −→ R, then the derivative of f is another function say f′ : [a,b] −→ R and defined by f′(c) = lim f(c+h)−f(c), ∀c ∈ (a,b). h→0 h Geometrically Speaking f′(c) is the slope of tangent to the curve f(x) at x = c. Lecture series on “Numerical techniques and MATLAB”, July 22-28, 2016 Dr. Sarvesh Kumar, IIST Trivandrum. 4
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