UNIT I VECTOR CALCULUS 
Derivatives: Gradient and Directional derivatives ᎓ Divergence and Curl of a vector field ᎓
Solenoidal and Irrotational of a vector ᎓ Green᎙s, Gauss divergence and Stoke᎙s theorems
(statements only) ᎓ Verification of theorems and application in evaluating line, surface and
volume integrals.
UNIT II ORDINARY DIFFERENTIAL EQUATIONS 
Higher order linear differential equations with constant coefficients ᎓ Method of variation of
parameters ᎓ Homogenous equation of Euler᎙s and Legendre᎙s type ᎓ Solution of system of
simultaneous linear first order differential equations with constant coefficients.
UNIT III PARTIAL DIFFERENTIAL EQUATIONS 
Solution of standard types of first order partial differential equations ᎓ Lagrange᎙s linear equation
᎓ Linear partial differential equations of second order with constant coefficients (Homogeneous
Problems).
UNIT IV FOURIER SERIES AND FOURIER TRANSFORMS 
Dirichlet᎙s conditions ᎓ General Fourier series ᎓ Odd and even functions ᎓ Fourier transform pair
᎓ Sine and Cosine transforms ᎓ P****val᎙s identity.
UNIT V LAPLACE TRANSFORMS 
Definition, properties, existence conditions ᎓ Transforms of elementary functions ᎓ Shifting
theorem ᎓ Transforms of derivatives and integrals ᎓Perio*** functions ᎓ Initial and final value
theorem ᎓ Inverse transforms ᎓ Application to solution of linear second order ordinary
differential equations with constant coefficients.

TEXT BOOKS
T1
Kreyszig.E, Advanced Engineering Mathematics, John Wiley and Sons, 10th Edition, New
Delhi 2016.
T2
Grewal.B.S., Higher Engineering Mathematics, Khanna Publishers, New Delhi, 44th
Edition, 2018.
REFERENCES
R1
Bali. N.P, Goyal. M. and Watkins. C., Advanced Engineering Mathematics, Firewall Media
(An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009.
R2 G.B.Thomas, Calculus, 12th Edition, Pearson Education India, 2015.

R3
Jain. R.K. and Iyengar. S.R.K., Advanced Engineering Mathematics, Narosa Publications,
New Delhi, 5th Edition, 2016.
R4
Peter V.O Neil, ᎜Advanced Engineering Mathematics᎝, 7th Edition, Cengage learning India
Pvt Ltd, New Delhi, 2012
R5
Srimanta Pal, Subodh C Bhunia, ᎜Engineering Mathematics᎝, Oxford University
Press,2015