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Note for Applied Mathematics-1 - M-1 By Amity Kumar

  • Applied Mathematics-1 - M-1
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2011 ENGNEERING MATHEMATICS – I Content CHAPTER UNIT I DIFFERENTIAL CALCULUS – I UNIT II DIFFERENTIAL CALCULUS – II UNIT III DIFFERENTIAL CALCULUS – III 2

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2011 UNIT - I DIFFERENTIAL CALCULUS – I Introduction: The mathematical study of change like motion, growth or decay is calculus. The Rate of change of given function is derivative or differential. The concept of derivative is essential in day to day life. Also applicable in Engineering, Science, Economics, Medicine etc. Successive Differentiation: Let y = f (x) --(1) be a real valued function. dy The first order derivative of y denoted by or y’ or y1 or ∆1 dx 2 The Second order derivative of y denoted by d yor y’’ or y2 or ∆2 dx 2 Similarly differentiating the function (1) n-times, successively, dny th the n order derivative of y exists denoted by n or yn or yn or ∆n dx The process of finding 2nd and higher order derivatives is known as Successive Differentiation. nth derivative of some standard functions: 1. Sol : y = eax y1 = a eax y2 = a2 eax Differentiating Successively yn = an eax ie. Dn[eax] = an eax For, a =1 Dn[ex] = ex 3

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