Can you provide me the details for Gate Entrance Exam?

Graduate Aptitude Test in Engineering (GATE) is an all India examination that above all tests the complete understanding of various undergraduate subjects in
Engineering and
Technology

GATE is conducted jointly by the
IIT Bombay,
IIT Delhi,
IIT Guwahati,
IIT Kanpur,
IIT Kharagpur,
IIT Madras and
IIT Roorkeeon

Syllabus Gate 2013
Here I am giving you the Gate Syllabus for Mechanical Engineering (ME)
Engineering Mathematics

Linear Algebra:
Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus:
Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Differential equations:
First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables:
Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series.

Probability and Statistics:
Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson,Normal and Binomial distributions.

Numerical Methods:
Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations.