Paper Code: ETMA-102	L          T          C
Paper: Applied Mathematics - II	3           1           4

UNIT - I

CALCULUS OF SEVERAL VARIABLES:

Partial differentiation, ordinary derivatives of first and second order in terms of partial derivaties, Euler’s theorem on homogeneous functions, change of variables, Taylor’s theorem of two variables and its application to approximate errors. Maxima and Minima of two variables, Langranges method of undermined multipliers and Jacobians.

UNIT - II

FUNCTIONS OF COMPLEX VARIABLES:

Derivatives of complex functions, Analytic functions, Cauchy-Riemann equations, Harmonic Conjugates, Conformal mapping, Standard mappings – linear, square, inverse and bilinear. Complex line integral, Cauchy’s integral theorem, Cauchy’s integral formula, Zeros and Singularities / Taylor series, Laurents series, Calculation of residues. Residue theorem, Evaluation and real integrals.

UNIT - III

VECTOR CALCULUS:

Scalar and Vector point functions, Gradient, Divergence, Curl with geometrical physical interpretations, Directional: derivatives, Properties.
Line integrals and application to work done, Green’s Lemma, Surface integrals and Volume integrals, Stoke’s theorem and Gauss divergence theorem (both without proof).

UNIT - IV

LAPLACE TRANSFORMATION:

Existence condition, Laplace transform of standard functions, Properties, Inverse Laplace transform of functions using partial fractions, Convolution and coinvolution theorem. Solving linear differential equations using Laplace transform. Unit step function, Impulse function and Periodic function and their transforms.

TEXT BOOKS:

1. E. Kresyzig, “Advanced Engineering Mathematics”, John Wiley and Sons. (Latest edition).
2. R. K. Jain and S. R. K. Iyengar, “Advanced Engineering Mathematics”, Narosa, 2003 (2nd Ed.).
3. Dr. A. B. Mathur, V. P. Jaggi, “Advanced Engineering Mathematics”, Khanna Publishers.

REFERENCE BOOKS:

1. V. V. Mitin, M. P. Polis and D. A. Romanov, “Modern Advanced Mathematics for Engineers”, John Wiley and Sons, 2001.
2. R. Wylie, “Advanced Engineering Mathematics”, McGraw-Hill, 1995.