# NIT Trichi 1st Year Syllabus Mathematics-II

Exact differential equations – different methods of finding the Integrating factor –– Clairaut’s

form– Singular solution – Applications – Newton’s Law of Cooling – Growth and Decay
problems.
Higher order linear differential equations with constant coefficients –Particular integrals for
xn eax, eax cos(bx), eax sin(bx) – Equation reducible to linear equations with constant
coefficients using x = et – Simultaneous linear equations with constant coefficients – Method
of variation of parameters – Applications – Electric circuit problems.
Gradient, Divergence and Curl – Directional Derivative – Tangent Plane and normal to
surfaces – Angle between surfaces –Solenoidal and irrotational fields – Line, surface and
volume integrals – Green’s Theorem, Stokes’ Theorem and Gauss Divergence Theorem (all
without proof) – Verification and applications of these theorems.
Analytic functions – Cauchy – Riemann equations (Cartesian and polar) –Properties of
analytic functions – Construction of analytic functions given real or imaginary part –
B.Tech. Syllabus (2009-‘10)
National Institute of Technology: Tiruchirappalli – 620 015. 10
Conformal mapping of standard elementary functions ( z2, ez, sinz, cosz, , z +
2
z
k ) and
bilinear transformation.
Cauchy’s integral theorem, Cauchy’s integral formula and for derivatives– Taylor’s and
Laurent’s expansions (without proof) – Singularities – Residues – Cauchy’s residue theorem
– Contour integration involving unit circle.
Text Books
1. Kreyszig, E., Advanced Engineering Mathematics, 8th edition, John Wiley Sons, 2001.
2. Grewal, B.S., Higher Engineering Mathematics, 40th edition, Khanna Publications, Delhi,
2007.
Reference Books
1. Apostol, T.M. Calculus, Volume I & II, 2nd Edition, John Wiley & Sons (Asia), 2005.
2. Greenberg, M.D. Advanced Engineering Mathematics, 2nd Edition, Pearson Education
Inc. (First Indian reprint), 2002.
3. Strauss. M.J, Bradley, G.L. and Smith, K.J. Calculus, 3rd Edition, Prentice Hall, 2002.