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# ME Mechanical Engineering

Section 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms;
evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in
one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional
derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.
Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with
constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat,
wave and Laplace’s equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula;
Taylor and Laurent series. Probability and Statistics: Definitions of probability, sampling
theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and
normal distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.