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picture1_Simple Equations Problems Pdf 182181 | Differentiation And Integration


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File: Simple Equations Problems Pdf 182181 | Differentiation And Integration
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 ...

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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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...Numericaldifferentiationandintegration lecture series on numerical techniques and programming in matlab vbspurvanchaluniversity jaunpur july by dr sarvesh kumar iist trivandrum differentiation basic problems derive a formula that approximates the derivative of function terms linear combination values may be known approximatethevalueofaderivativeofafunctiondenedbydiscrete data solution approaches use taylor expansion pass polynomial through given differentiate interpolating applications to solve ordinary partial differential equations first let f r then is another say dened c lim h b geometrically speaking slope tangent curve x at...

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