Mechanical Engineering

Section 1:
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 Greens theorems.
Differential equations
First order equations (linear and non-linear) 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, and Taylor and Laurent series.
Probability and Statistics
Definitions of probability, sampling theorems, conditional probabilityMean, 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 Simpsons rules, and Single and multi-step methods for differential equations.