# GITAM University Engineering Mathematics III Syllabus

B.Tech. (BT) V Semester
ENGINEERING MATHEMATICS-III
Course Code : EURBT 501 Category: MT
Credits: 3 Hours : 3 per week
UNIT-I
Partial Differential Equations and Applications: Introduction. First and second
order equations, method of separation of variables. Vibrations of a stretched stringwave
equation.
UNIT-II
One-dimensional and two-dimensional heat flow equations, solution of Laplace
equation. Laplace equation in polar coordinates.
UNIT-III
Vector Calculus: Scalar, Vector fields, Gradient, Divergence, curl, directional
derivative, identities, irrotational and solenoidal vector fields, line integral, surface
integral and volume integral, introduction of orthogonal curvilinear coordinates.
Cylindrical, spherical and polar coordinates.
UNIT-IV
Complex Analysis: Differentiability, Cauchy-Riemann equations, analytic functions
Cauchy’s Theorem, Cauchy’s integral formula, Taylor and Laurent expansions,
(without proofs), singularities, Residue Theorem, contour integration.
UNIT-V
Geometric representation of f(z), conformal transformation, some standard
transformations: (I)w=z+c, (2) cz, W=I/Z u = (az+b) / (cz+d), W = Z2 and W = CZ

Text Book: Scope as given in:
1. Higher Engineering Mathematics (34 edition, 1998) by B.S. Grewal, Khanna
Publications, New Delhi –110 006, 34 edition, 1998.

Reference:

1. Higher Engineering Mathematics, by M.K.Venkataraman, National Pub Co, Madras.
2. Advanced Engg Maths, by Erwin Kreyszig, Wiley Eastern Pvt. Ltd., New Delhi- 49.
3. Engineering Maths by P.P.Gupta, Krishna Prakasam Media P Ltd., Meerut Vol-2.