Name of the Subject – Mathematics

Cartesian, cylindrical, polar, spherical polar coordinates, direction ratios and direction cosines, equations of planes and straight lines shortest distance, coordinate transformations, spheres, cones, cylinders, ellipsoids, paraboloids, and hyperboloid

Standard Equations

With illustration, tangent, planes, and normals

Continuity and differentiability of functions of a single variable with terminology, properties of continuous functions, geometrical illustrations, applications of differentiation to approximate computations, successive differentiation, Leibniz rule

Rolle’s theorem, Cauchy’s mean value theorem (Lagrange mean value theorem as a special case)

Taylor and Maclaurin expansions, L-hospital rule, reviews of maxima and minima of function of single variable, concavity and convexity of curve, points of inflexion, asymptotes, and curvature

Limit, continuity, and differentiability of function, geometrical interpretations, differentials, derivatives of composite and implicit function, derivative of higher orders and their commutatively, Euler’s theorem on homogeneous function

Taylor expansion of functions of several variables, maxima and minima of functions of several variables

Lagrange method of multipliers

Riemann integrals (upper and lower sums), definite integral as the limit of a sum, fundamental theorem of integral calculus, mean value theorems, evaluation of definite integrals, reduction formula, convergence of improper integrals, tests of convergence

Beta and gamma functions, elementary properties, differentiation under integral sign, differentiation of integrals with variable limits, Leibniz rule, integrals dependent on a parameter applications, rectification, double and triple integrals

Computation of surfaces and volumes, changes of variables in double integrals, Jacobean transformations, integrals dependent on parameters application

First-order equation variable separable, exact, homogeneous, linear and Bernoulli’s form, second-order equations with constant coefficients, Euler equations, methods of their solution, dependence, and independence of solutions

Wronskian systems of first-order equations (simple type)

Scalar and vector fields, level surfaces, directional derivative, gradient, Curl, divergence, Laplacian, line and surface integrals, theorem of Greene, Gauss, and Stokes, orthogonal curvilinear coordinates, infinite series

Sequence and series their convergence and divergence, test of convergence, power series-uniform, and absolute convergence

Algebra of matrices, vector space, the linear dependence of vectors, rank and inverse of a matrix, solutions of algebraic equations, consistency conditions, eigenvalue and eigenvectors, similarity transformation reduction to a diagonal matrix

Its convergence, Dirichlet conditions, half range series

Name of the Subject – Engineering Mechanics

dealization of mechanics, concept of rigid body

External forces (body forces and surface forces), laws of mechanics

Equality and equivalence of vectors, free and bound vectors, principle of transmissibility of forces, moment of force about a point and about a line, couple and moment of a couple, couple moment as a free-vector, addition and subtraction of couples

Statically equivalent force systems, simples equivalent of a system of forces

Force analysis, free body diagram, equations of equilibrium and their applications to the various systems of forces, plane trusses

Friction on dry surfaces, static, kinetic, and rolling friction, applications to inclined planes, wedge and blocks and belts, and pulleys

Rectilinear and curvilinear translations, normal and tangential components of acceleration, projectile motion on a smooth vertical curve

Linear impulse and linear momentum, the central impact of elastic, semi-elastic, and plastic bodies

Angular velocity and angular acceleration, effective forces on a rigid body, D’ Alembert’s principle-application to highways and railway tracks, instantaneous centre of rotation, compound pendulum, the centre of percussion, rotation of rigid bodies

Rolling motion, the plane motion of rigid bodies, simple application-four bar mechanism

Work done by forces and couples, potential, elastic, and kinetic energy, work-energy, conservation of energy, the concept of power and efficiency

Name of the Subject – Technical

Subject, Word and Concord

Tense

Voice

Synthesis

Common Errors

Vocbulary

Unseen Passage

Drafting official and business letters

Grafting circulars and official orders/ instructions

Drafting minutes and agenda of the meeting

Elementary Theory of Phonetics

Importance of reports in the present-day industrial set-up

Classification of reports

Writing of reports: (a) Format, (b) Mechanics of language