# C-14 III-SEM ENGINEERING MATHEMATICS – II

ENGINEERING MATHEMATICS – II
(Common to all Branches)

Subject Title                          :         Engineering Mathematics-II
Subject Code                          :         Common-301
 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
Unit-I
1.0       Use Indefinite Integration to solve engineering problems
1.1       Explain the concept of Indefinite integral as an anti-derivative.
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 Sinmq  Cosn 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 ex [f(x) + f ¢(x)] dx.

Unit-II
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 co-varience.
4.9       Explain coefficient of correlation and its properties
4.10     Calculate the coefficient of correlation between two variables.
4.11     Find rank correlation co-efficient.

COURSE CONTENT
Unit-I
Indefinite Integration:
1. Integration regarded as anti-derivative – Indefinite integral of standard functions.    Properties of indefinite integral. Integration by substitution or change of variable. Integrals of the form
sinmq. cosn 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.

Unit-II
Definite Integral and its applications:
2.  Definite integral-fundamental 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 equation-order and degree of a differential equation- formation of differential equations-solution of differential equation of first order, first degree: variable-separable, 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 co-efficient.

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 McGraw-Hill
4.   Statistics, 4/e, Schaum’s Outline Series (SIE),  McGraw-Hill

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