Unit - I : Differential Calculus-I
Leibnitz theorem, Partial differentiation, Eulers theorem, Curve tracing, Change of variables, Expansion of
function of several variables.
Unit – II : Differential Calculus-II
Jacobian, approximation of errors, Extrema of functions of several variables, Lagranges method of multipliers
(Simple applications).
Unit – III : Matrices
Elementary row and column transformation, Rank of matrix, Linear dependence, Consistency of linear system
of equations and their solution, Characteristic equation, Caley-Hamition theorem, Eigen values and eigen
vectors, Diagonalisation, Complex and unitary matrices, Application of matrices to engineering problems.
Unit – IV : Multiple Integrals
Double and triple integral, Change of order, Change of variables, Beta and Gamma functions, Application to
area, volume, Dirichlet integral and applications.
Unit – V : Vector Calculus
Point function, Gradient, divergence and curl of a vector and their physical interpretations, Line, surface and
volume integrals, Statement and problems of Green’s, Stoke’s and Gauss divergence theorems (without proof).
Test Books:-
1. B.V.Ramana, Higher Engineering Mathmatics, Tata Mc Graw-Hill Publishing Company Ltd., 2008.
2. R.K.Jain & S.R.K.Iyenger, Advance Engineering Mathematics, Narosa Publishing House, 2002.
Reference Books:-
1. B.S.Grewal, Engineering Mathematics, Khanna Publishers, 2004.
2. B.S.Grewal, Higher Engineering Mathematics, Khanna Publishers, 2005.
3. E.Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2005.
4. C.Ray Wylie & Louis C. Barrett, Advanced Engineering Mathematics, Tata Mc Graw-Hill Publishing
Company Ltd. 2003
5. Peter V. O’Neil, Advanced Engineering Mathematics, Thomson (Cengage) Learning, 2007
EAS-203 - MATHEMATICS –II
Unit - I : Differential Equations
Linear differential equations of nth order with constant coefficients, Complementary functions and particular
integrals, Simultaneous linear differential equations, Solution of second order differential equation by changing
dependent and independent variables, Method of variation of parameters, Applications to engineering problems
(without derivation).
Unit – II : Series Solution and Special Functions
Series solution of ordinary differential equations of 2nd order with variable coefficients (Frobenius Method),
Bessel and Legendre equations and their series solutions, Properties of Bessel functions and Legendre
polynomials.
Unit – III : Laplace Transform
Laplace transform, Existence theorem, Laplace transform of derivatives and integrals, Inverse Laplace
transform, Unit step function , Dirac delta function, Laplace transform of periodic functions, Convolution
theorem, Application to solve simple linear and simultaneous differential equations.
Unit – IV : Fourier Series and Partial Differential Equations
Periodic functions, Trignometric series, Fourier series of period 2 π , Eulers formulae, Functions having
arbitrary period, Change of interval, Even and odd functions, Half range sine and cosine series, Harmonic
analysis.
Solution of first order Lagrange’s linear partial differential equatins, Linear partial differential equations with
constant coefficients of 2nd order and their classifications - parabolic, elliptic and hyperbolic with illustrative
examples.
Unit – V : Applications of Partial Differential Equations
Method of separation of variables for solving partial differential equations, Wave equation up to two-
dimensions, Laplace equation in two-dimensions, Heat conduction equations up to two-dimensions, Equations
of transmission lines.
Test Books:-
1. B.V.Ramana, Higher Engineering Mathmatics, Tata Mc Graw-Hill Publishing Company Ltd., 2008.
2. R.K.Jain & S.R.K.Iyenger, Advance Engineering Mathematics, Narosa Publishing House, 2002.
Reference Books:-
1. B.S.Grewal, Engineering Mathematics, Khanna Publishers, 2004.
2. B.S.Grewal, Higher Engineering Mathematics, Khanna Publishers, 2005.
3. E.Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2005.
4. C.Ray Wylie & Louis C. Barrett, Advanced Engineering Mathematics, Tata Mc Graw-Hill Publishing
Company Ltd. 2003
5. Peter V. O’Neil, Advanced Engineering Mathematics, Thomson (Cengage) Learning, 2007.
6. G.F.Simmons, Differential Euations, Tata Mc Graw-Hill Publishing Company Ltd. 1981.
7. Chandrika Prasad, Advanced Mathematic for Engineers, Prasad Mudranalaya,1996.
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