10MAT41 Engineering Mathematics IV syllabus for CV

Numerical solution of ordinary differential equations of first order and first degree;
Picard’s method, Taylor’s series method, modified Euler’s method,
Runge-kutta method of fourth-order. Milne’s and Adams - Bashforth
predictor and corrector methods (No derivations of formulae).

Numerical solution of simultaneous first order ordinary differential equations: Picard’s method,
Runge-Kutta method of fourth-order.
Numerical solution of second order ordinary differential equations: Picard’smethod,
Runge-Kutta method and Milne’s method.

Function of a complex variable, Analytic functions-Cauchy-Riemann
equations in cartesian and polar forms. Properties of analytic functions.

Application to flow problems- complex potential, velocity potential,equipotential lines,
stream functions, stream lines.

Conformal Transformations: Bilinear Transformations. Discussion of Transformations:
w = z² , w = e^z , w = z + ( a² / z ) .
Complex line integrals- Cauchy’s theorem and Cauchy’s integral formula.

Solution of Laplace equation in cylindrical and spherical systems leading
Bessel’s and Legendre’s differential equations, Series solution of Bessel’s
differential equation leading to Bessel function of first kind. Orthogonal property of Bessel
functions. Series solution of Legendre’s differential equation leading to Legendre polynomials,
Rodrigue’s formula.

Probability of an event, empherical and axiomatic definition, probability associated with set theory,
addition law, conditional probability,multiplication law, Baye’s theorem.

Random variables (discrete and continuous), probability density function,cumulative density function.
Probability distributions – Binomial and Poisson distributions;
Exponential and normal distributions.

Sampling, Sampling distributions, standard error, test of hypothesis for means,
confidence limits for means, student’s t-distribution. Chi -Square distribution as a
test of goodness of fit