Arni University::: B.Tech Mechanical II SEMESTER

ARNI UNIVERSITY
Campus: Kathgarh (Indora), Himachal Pradesh-176401,

01893-302000, 01893-302075, www.arni.in; Email: info@arni.in
:: B.Tech Mechanical > II SEMESTER >
Click to Print
The detailed Syllabus

Paper Code : (AS-203)
Paper Name : (Engineering Mathematics-II)
L-T-P(3-10)
UNIT-I
Matrices
&
its
Application:
Rank of a matrix, elementary transformations, elementary matrices, inverse using
elementary transformation, normal form of a matrix, linear dependence and its dependence
of vectors, consistency of linear system of equations, linear and orthogonal transformations,
Eigen values and Eigen vectors, properties of Eigen values , cayley Hamilton theorem and
its applications.
UNIT II
Ordinary
Differential
Equations
&its
Application:
Exact differential equations, Equations reducible to exact differential equations.
Applications and Differential equations of first order and first degree to simple electric
circuits, Newtons law of cooling ,heat flow and orthogonal trajectories.
Linear
differential
equations
of
second
and
higher
order:
complete solution , complementary function and particular integral, method of variation of
parameters to find particular integral ,Cauchys and Legendres linear equations,
simultaneous linear equation with constant co-efficient. Applications of linear differential
equations to simple pendulum, oscillatory electric circuits.
UNIT III
Laplace Transforms and its Applications: Laplace transforms of elementary functions,
properties of laplace transforms, existence conditions, transforms of derivatives, transforms
of integrals, multiplications by t division by t. Evaluation of integrals by Laplace
transforms. Laplace transform of unit step function, unit impulse function and periodic
function, inverse transforms , convolution theorem, application to linear differential

equations and simultaneous linear differential equations with constant coefficients.
UNIT IV
Partial Differential Equations and its Applications: Formation of partial differential
equations, Lagrange linear partial differential equation, first order non-linear partial
differential equations , Charpits method ,Method of separation of variables and its
application to wave equation and one dimensional heat equation, two dimensional heat law,
steady state solutions only.
REFERENCE BOOKS:
1. Engineering mathematics by B. S Grewal
2. Engineering mathematics by N.O Bali
3. Spectrum by D.R Sharma
ARNI UNIVERSITY
Campus: Kathgarh (Indora), Himachal Pradesh-176401,
01893-302000, 01893-302075, www.arni.in; Email: info@arni.in
:: B.Tech Mechanical > I SEMESTER >
Click to Print
The detailed Syllabus

Paper Code : (AS-103)
Paper Name : (Engineering Mathematics-I )
L-T-P(3-1-0)
UNIT-I
Applications of Differentiation : Taylors & Maclaurins series, Expansion by use of
known series, Expansion by forming a differential equation, Asymptotes, Curvature, Radius
of Curvature for Cartesian, Parametric & polar curves, Centre of curvature & chord of
curvature, Tracing of Cartesian & polar curves (standard curves).
UNIT II
Partial Differentiation & Its Applications: Functions of two or more variables Partial
derivatives, Total differential and differentiability, Derivatives of composite and implicit
functions, change of variables. Homogeneous functions, Eulers theorem, Jacobian,
Taylors & Maclaurins series for functions of two variables (without proof), Errors and
approximations, Maxima-minima of functions of two variables, Lagranges method of
undetermined multipliers, Differentiation under the integral sign.
UNIT III
Multiple Integrals and their Applications: Double integral, change of order of integration
Double integral in polar coordinates, Applications of double integral to find area enclosed
by plane curves and volume of solids of revolution. Triple integral, volume of solids,
change of variables, Beta and gamma functions and relationship between them.
UNIT IV
Vector Calculus: Differentiation of vectors, scalar and vector point functions Gradient of a
scalar field and directional derivative, divergence and curl of a vector field and their
physical interpretations, Del applied twice to point functions, Del applied to product of
point functions. Integration of vectors, line integral, surface integral, volume integral,
Greens, Stokes and Gauss divergence theorems (without proof), and their simple
applications.

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ARNI UNIVERSITY

Campus: Kathgarh (Indora), Himachal Pradesh-176401,

The detailed Syllabus

function, inverse transforms , convolution theorem, application to linear differential

3. Spectrum by D.R Sharma

The detailed Syllabus

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