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Applied Mathematics – I
2011
Applied Mathematics – I
LECTURE NOTES
1

2011
ENGNEERING MATHEMATICS – I
Content
CHAPTER
UNIT I
DIFFERENTIAL CALCULUS – I
UNIT II
DIFFERENTIAL CALCULUS – II
UNIT III
DIFFERENTIAL CALCULUS – III
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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
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