Vector Algebra: Vectors and scalars, vector addition, resolution of vectors, scalar components, unit vectors, vector representation in three dimensions, scalar and vector product of two vectors.

Determinants: Determinants; properties, solution of a system of linear equations by Cramer’s rule.

Complex numbers: Complex Numbers, De Moiver’s theorem, exponential values of sines and cosines, hyperbolic functions.

Differential Calculus: Differentiation and integration of hyperbolic functions. Rolle’s theorem, mean Value theorem, Taylor’s and Maclaurin’s series. Maxima and Minima of function of one variable.

Integral Calculus: Properties of Definite Integrals. Fundamental theorem of integral calculus. Arc length and surface areas of plane curves. Volume and Surface Area of Solids of revolution. Centre of gravity.

Geometrical Optics: Lens aberrations; longitudinal chromatic aberration, lateral chromatic aberration, two lenses in contact, two lenses separated by a distance; Monochromatic aberration; spherical aberration, coma, oblique astigmatism, curvature and field of distortion.

Interference: Relation between phase and path difference; coherent sources; Young’s Double slit, Fresnel’s Biprism, Lloyd’s single mirror; position of Bright and Dark fringes, fringe width. Displacement of fringes; Newton’s rings.

Diffraction: Fresnel and Fraunhofer diffraction, single slit and double slit diffraction, diffraction grating; introduction to reflection and transmission, resolution and Raleigh criterion, resolving power of grating.

Polarisation: Concepts, Brewester’s law, double refraction, optic axis; Nicol prism. Laurent’s and Bi-quartz’s polarimeter.

Fibre Optics: Basic principle and application of optical fibres.

Introduction to Lasers: Stimulated absorption, spontaneous emission and stimulated emission. Characteristics of Laser light. Einstein’s A and B coefficients. Population inversion’ Ruby laser, helium-neon laser, argon ion laser, CO2 laser, semi conductor lasers.

Acoustics: Simple harmonic motion, free and damped vibration, analogy with electric circuits, forced vibration, Resonance; amplitude resonance and velocity resonance and energy intake, absorption of sound; Sabine’s formula (statement only), acoustic properties of buildings, production and application of ultrasonics.

Magnetism & Electricity: Biot-Savart law; magnetic fields due to a long straight conductor, a narrow circular coil, on the axis of a solenoid. Magnetic circuits, magnetomotive force, reluctance. Alternative current; r.m.s. value, mean value of an a.c. current. Applications of a.c. to (i) a pure resistance, (ii) a pure inductance, (iii) a capacitor, (iv) an L-R circuit. Impedence triangle and power triangle. Application of a.c. to (i) a C-R circuit and (ii) an L-C-R circuit in series.

Chemical Bonds: Types of chemical bonds; ionic, covalent, coordination bonds. Theory of bonding in metals; free electron theory, valence bond theory, molecular orbital theory. Hydrogen bonding; intermolecular and intramolecular hydrogen bonding. Solid state chemistry; laws of crystallography, laws of constancy of interfacial angle, law of rationality of indices, Weiss and Miller indices, law of symmetry; plane of symmetry, axis of symmetry, centre of symmetry. Crystal lattice and unit cell. Examples of cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal and rhombohedral crystals. Body centered and face centred lattices.

Polymer Chemistry: Natural and synthetic polymers, Organic and inorganic polymers, thermoplastic and thermosetting polymers, plastics, elastones, fibres and liquid resins. Addition and condensation polymers. Structure of polymers.

Chemical Kinetics: Reaction rate and rate laws, rate constant, order of a chemical reaction; zero, first and second order reaction.

Corrosion: Types of corrosion, theories of corrosion, factors affecting corrosion, protection from corrosion.

Water Treatment: Types and degrees of hardness, softening of water; lime soda process, treatment of boiler feed water.

Fuel and Combustion: Calorific value, determination of calorific value, analysis of coal.

Environmental protection: Types and sources of air pollutants, pollution control techniques. Smog formation, acid rain, depletion of ozone layer.

Grammar. Usage, essays on current topics, précis, letter and technical presentation and technical report writing.

Statics: Composition ad resolution of forces, equilibrium, Lami’s theorem; Coplanar Non-concurrent forces, moment, Varignon’s theorem, couple, resultant of force systems. Reactions at supports of beams. Analysis of pinjointed plane frames; method of joints, method of section.

Friction: Laws of friction; angle of friction, angle of repose and cone of friction, simple applications to wedges, ropes.

Centroid and Moment of Inertia: Determination of centroids of simple figures,theorems of moments of inertia, determination of moments of inertia of simple shapes.

Dynamics: Kinematics; Linear motion with uniform velocity and uniform acceleration. Projectiles; inclined projections on level ground, projections on inclined plane, Relative velocity.

Kinetics: D’Alembert’s principle, Impulse momentum, simple applications to motion of connected bodies.

Circular motion of rigid bodies: acceleration, motion on level ground, banking of roads and super elevation of rails, designed speed, skidding and overturning on banked roads.

Stress-strain diagram, Hooke’s law, Poisson’s ratio, principal stresses, Mohr circle in two dimensions. Thermal stresses.

Flexure formulae, bending moment and shear force diagram of cantilever, simply supported and overhanging beams with concentrated, uniformly distributed and uniformly varying loads. Deflection in simply supported and cantilever beams; double integration method.

Thin cylinder under internal pressure.

Applied Electricity and magnetism: Electrical charge; potential, flux density, magnetic field; Direct current – emf, Current and Ohm’s law; resistivity; Kirchhoff’s law. Wheatstone bridge, potentiometer; Elements of Network Analysis; delta-star transformation. Magnetomotive force, magnetic reluctance, Ampere turns; hysterisis; self and mutual inductance, eddy currents. Alternating current; instantaneous, average and r.m.s. values; Vector representation; simple circuit calculations; response of resistance, inductance and capacitance to D.C. and A.C. voltage sources. Series and parallel resonance of LRC Circuits. Power factor.

Electrical Machines: Elements of construction, operation and characteristics of D.C. and A.C. Generators and motors; starters. Transformers, Introduction to variable speed drives.

Electrical Measuring Instruments: Ammeter, Voltmeter, Wattmeter, energy meter, recorders.

Electronics: Semi Conductors: P and N type, P-N diodes, P-N-P and N-P-N transistors.

Diodes and transistor circuits; single phase, half wave and full wave rectifier, bridge rectifiers and filtering circuits. Transistor biasing and stabilisation.

Transistor as an amplifier. Common emitter amplifier, the emitter follower. Feedback amplifier; positive and negative feedback. The operational amplifier (TC). Use of operators of amplifier as Invertor. Adder, integrator, differentiator.

Push-Pull inverter circuits.

Atomic structure and types of bonding between atoms: Bohr’s atomic model – electronic configuration of atoms, periodic classification of elements. Binding energy; ionic bonds, covalent bonds, material properties having these bonds. Electro negativity. Metallic bond – materials properties having this bond. Intermolecular forces.

Concepts of crystal geometry: space lattice – cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic and triclinic. Unit cell parameters to specify each crystal system. Crystal directions and planes, Miller indices.

Binding in solids: covalent, ionic, metallic and molecular bonding. Crystal symmetry and structure. Crystalline imperfections. Point imperfections and line imperfections or dislocations, edge and screw dislocations, slip planes. Surface imperfections. Structure in silica and silicates; polymorphism in metals and ceramics; Amorphous materials – glass and polymer.

Alloys: binary phase diagrams of important alloy systems, dendrite structure, lever rule, solid solutions, eutectic, peritectic, eutectoid and peritectoid reactions. Intermetallic compounds, sigma & other phases.

Mechanical deformation of materials: elastic and anealstic; plastic deformation and creep, slip and twin, dislocation theory, critical resolved sheer stress, deformation in polycrystalline material. Bauschinge’s effect and