Engineering mathematics for first year is a course that introduces students to the mathematical concepts and techniques that are essential for studying engineering. It covers a wide range of topics, including:
Calculus: This includes concepts such as derivatives, integrals, limits, and vector calc...
Dr. V. Lokesha
Professor and Head
DEPARTMENT OF MATHEMATICS
ACHARYA INSTITUTE OF TECNOLOGY
Soldevanahalli, Bangalore – 90
10 MAT11
1
,Engineering Mathematics – I Dr. V. Lokesha
2011
ENGNEERING MATHEMATICS – I
Content
CHAPTER
UNIT I DIFFERENTIAL CALCULUS – I
UNIT II DIFFERENTIAL CALCULUS – II
UNIT III DIFFERENTIAL CALCULUS – III
10 MAT11
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,Engineering Mathematics – I Dr. V. Lokesha
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
the n order derivative of y exists denoted by n or yn or yn or ∆n
th
dx
The process of finding 2nd and higher order derivatives is known as Successive Differentiation.
nth derivative of some standard functions:
1. y = eax
Sol : y1 = a eax
y2 = a2 eax
Differentiating Successively
yn = an eax
ie. Dn[eax] = an eax
For, a =1 Dn[ex] = ex
10 MAT11
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, Engineering Mathematics – I Dr. V. Lokesha
2011
10 MAT11
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