Equivalent force systems. Equations of equilibrium. Two dimensional frames and trusses. Free body diagrams. Friction forces. Particle kinematics and dynamics. Limit, continuity, and differentiability of functions of several variables. Partial derivatives and their geometrical interpretations. Implicit functions. Derivatives of higher order and their commutativity. Euler’s theorem on homogeneous functions and harmonic functions. Tailors expansion for functions of several variables. Maxima and minima of functions of several variables. Lagrangian method of multipliers. Ordinary differential equations: first order, separable, exact, homogeneous, linear and Bernoulli’s form. Matrix algebra: vector space, linear dependence, rank and inverse of matrix. Solution of algebraic equations: consistency conditions, eigen values and eigen vectors. Probability and Statistics: random variables, distributions, mathematical expectation, Bayes’ Theorem, central limit theorem, sample distributions, estimation, hypothesis testing. Correlation. Regression: simple, multiple, and partial.