Unit I
DIFFERENTIAL CALCULUS :
Expansion of functions by
Maclaurin’s and Taylor’s theorem. Partial differentiation, Euler’s
theorem and its application in
approximation and errors, Maxima and Minima of function of
two variables, Curvature : Radius
of curvature, centre of curvature.
Unit II
INTEGRAL CALCULUS :
Definite Integrals : Definite
Integrals as a limit of a sum , its application in Summation of
series, Beta and Gamma Functions
, Double and Triple Integrals, Change of Order of
Integration, Area,Volume and
Surfaces using double and triple Integral.
Unit III
DIFFERENTIAL EQUATIONS :
Solution of Ordinary Differential
Equation of first order and first degree for Exact
differential Equations, Solution
of Ordinary Differential Equation of first order and higher
degree (solvable for p, x and y,
Clairauts Equation), Linear Differential Equations with
Constant Coefficients, Cauchy’s
Homogeneous differential Equation, Simultaneous
differential Equations, Method of
Variation of Parameters
Unit IV
MATRICES :
Rank, Solution of Simultaneous
equation by elementary transformation, Consistency of
System of Simultaneous Linear
Equation, Eigen Values and Eigen Vectors, Cayley-Hamilton
Theorem and its Application to
find the inverse
Unit V
Algebra of Logic, Boolean
Algebra, Principle of Duality, Basic Theorems, Boolean
Expressions and Functions.
Elementary Concept of Fuzzy Logic
Graph Theory : Graphs, Subgraphs,
Degree and Distance, Tree, cycles and Network.
References:
( i ) Advance Engg. Mathematics.
By Ramana, Tata McGraw hill.
(ii) Higher Engineering
Mathematics by BS Grewal, Khanna Publication
(iii) Advance Engineering Mathematics
by D.G.Guffy
(iv) Engineering Mathematics by S
S Sastri. P.H.I.
(v) Mathematics for Engineers by
S.Arumungam, SCITECH Publuication
(vi) Advanced Engineering Mathematics by Erwin
Kreyszig, Wiley India
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