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ENGINEERING
MATHEMATICS – II
(Common to all Branches)
Subject Title : Engineering
MathematicsII
Subject Code : Common301
S. No

Major Topic

No of Periods

Weightage of
Marks

Short Type

Essay Type


Unit  I

R

U

App

R

U

App


1

Indefinite Integration

18

34

2

1

0

1

1

1/2

Unit  II


2

Definite Integration and its applications

17

31

0

1

1

0

1

1 1/2

Unit  III


3

Differential Equations of first order

15

29

2

1

0

1/2

1/2

1

Unit  IV


4

Statistical Methods

10

16

1

1

0

1

0

0

Total

60

110

5

4

1

2 1/2

2 1/2

3


Marks:

15

12

3

25

25

30


R:

Remembering
type

40 marks


U:

Understanding
type

37 marks


App:

Application
type

33 marks

Periods per week : 04
Periods per Semester : 60
Blue print
OBJECTIVES
Upon completion of the subject the student shall be
able to
UnitI
1.0 Use Indefinite Integration to solve engineering problems
1.1 Explain the concept of Indefinite integral
as an antiderivative.
1.2 State the indefinite integral of standard
functions and properties of Integrals ò (u + v) dx
and ò ku dx where
k is constant and u, v are functions of x.
1.3 Solve integration problems involving
standard functions using the above rules.
1.4 Evaluate integrals involving simple
functions of the following type by the method of substitution.
i) ò f(ax + b) dx where f(x) dx is in standard form.
ii) ò [f(x)]^{n } f ¢(x) dx
iii) ò f ¢(x)/[f(x)] dx
iv) ò f {g(x)} g ¢(x) dx
1.5 Find the Integrals of tan x, cot x, sec x and cosec
x using the above.
1.6 Evaluate
the integrals of the form ò Sin^{m}q
Cos^{n }q. dq where m and n are positive integers.
1.7 Evaluate integrals of powers of tan x and sec x.
1.8 Evaluate the
Standard Integrals of the functions of the type
1.9 Evaluate the integrals of
the type
.
1.10 Evaluate integrals using decomposition
method.
1.11 Evaluate integrals using integration by
parts with examples.
1.12 State the Bernoulli’s rule for evaluating
the integrals of the form.
1.13 Evaluate the integrals of the form ò e^{x }[f(x)
+ f ¢(x)] dx.
UnitII
2.0 Understand
definite integral and use it in engineering applications
2.1 State the fundamental theorem of integral
calculus
2.2 Explain the concept of definite integral.
2.3 Calculate the definite integral over an
interval.
2.4 State various properties of definite
integrals.
2.5 Evaluate simple problems on definite
integrals using the above properties.
2.6 Explain definite integral as a limit of
sum by considering an area.
2.7 Find the areas under plane curves and area
enclosed between two curves using integration.
2.8 Obtain the volumes of solids of
revolution.
2.9 Obtain the mean value and root mean square
value of the functions in any given
interval.
2.10 Explain the Trapezoidal rule, Simpson’s 1/3 rules for approximation
of integrals and
provide some examples.
Unit III
3.0 Solve
Differential Equations in engineering problems.
3.1 Define a Differential equation, its order,
degree
3.2 Form a differential equation by
eliminating arbitrary constants.
3.3 Solve
the first order first degree differential equations by the following methods:
i. Variables
Separable.
ii. Homogeneous
Equations.
iii.
Exact Differential Equations
iv. Linear differential equation of the form
dy/dx + Py = Q,
where
P and Q are functions of x or constants.
iv.
Bernoulli’s Equation (Reducible to linear form.)
3.4 Solve simple problems leading to
engineering applications
Unit IV
4.0 Use Statistical Methods as a tool in data
analysis.
4.1 Recall the measures of central tendency.
4.2 Explain the significance of measures of
dispersion to determine the degree of
heterogeneity of the data.
4.3 Find the measures of dispersion – range,
quartile deviation, mean deviation, standard
deviation for the given data.
4.4 Explain the merits and demerits of the
above measures of dispersion.
4.5 Express relationship between measures of
dispersion
4.6 Find the coefficient of variation
4.7 Explain bivariate data.
4.8 Explain the concept of correlation between
two variables and covarience.
4.9 Explain coefficient of correlation and its
properties
4.10 Calculate the coefficient of correlation
between two variables.
4.11 Find rank correlation coefficient.
COURSE CONTENT
UnitI
Indefinite
Integration:
1. Integration regarded as
antiderivative – Indefinite integral of standard functions. Properties of indefinite integral.
Integration by substitution or change of variable. Integrals of the form
sin^{m}q. cos^{n }q. where m and n
are positive integers. Integrals
of tan x, cot x, sec x, cosec x and
powers of tan x, sec x by substitution.
Evaluation
of integrals which are reducible to the following forms :
Integration by decomposition
of the integrand into simple rational, algebric functions. Integration by parts
, Bernoulli’s rule.
UnitII
Definite Integral and its applications:
2.
Definite integralfundamental theorem of integral calculus, properties
of definite integrals, evaluation of
simple definite integrals. Definite
integral as the limit of a sum. Area under plane curves – Area enclosed between two
curves. Volumes of solids of revolution. Mean and RMS values of a function on a given interval.
Trapezoidal rule, Simpson’s 1/3 rule to evaluate an approximate value of a define integral.
Unit III
Differential Equations:
3. Definition
of a differential equationorder and degree of a differential equation
formation of differential equationssolution of differential equation of first
order, first degree: variableseparable, homogeneous, exact, linear
differential equation, Bernoulli’s equation.
Unit –IV
Statistical Methods:
4. Revise
measures of central tendency, measures of dispersion: range, quartile
deviation, mean deviation, standard
deviation for the given data, merits and demerits, relationship between measures of dispersion, coefficient of
variation, bivariate data, concept of correlation, covariance, coefficient of correlation and its
properties, rank correlation coefficient.
Reference
Books:
1. Integral Calculus Vol.I, by M.Pillai and Shanti Narayan
2. Thomas’ Calculus, Pearson Addison –Wesley Publishers
3. Statistical Methods Vol.I, Das,
Tata McGrawHill
4. Statistics, 4/e, Schaum’s Outline Series (SIE), McGrawHill