| Chapters | Subtopics |
| Engineering Mathematics Syllabus |
| Linear Algebra | Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors. |
| Calculus | Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series. |
| Vector Calculus | Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems. |
| Differential Equations | Linear and non-linear first-order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations. |
| Probability and Statistics: | Probability and sampling theorem, Conditional Probability, Probability Density Function, Mean, median, mode and standard deviation; Random variables; Exponential, Poisson, normal and binomial distributions; Correlation and regression analysis |
| Numerical Methods | Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations. |
Mechanical Engineering Applied Mechanics and Design |
| Engineering Mechanics | Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum (linear and angular) and energy formulations; impact. |
| Strength of Materials | Stress and strain, stress-strain relationship and elastic constants, Mohr's circle for plane stress and plane strain, thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler's theory of columns; strain energy methods; thermal stresses. |
| Theory of Machines | Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels. |
| Vibrations | Free and forced vibration of single degree of freedom systems; effect of damping; vibration isolation; resonance, critical speeds of shafts. |
| Design | Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints, shafts, spur gears, rolling and sliding contact bearings, brakes and clutches. |
| Fluid Mechanics and Thermal Sciences |
| Fluid Mechanics | Fluid properties; fluid statics, manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli's equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc |
| Heat-Transfer | Modes of heat transfer; one-dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods |
| Thermodynamics | Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle. Irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion. |
| Applications | Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning: Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air: psychrometric chart, basic psychrometric processes. |
| Turbomachinery | Peltonwheel, Francis and Kaplan turbines - impulse and reaction principles, velocity diagrams. |
| Manufacturing and Industrial Engineering |
| Engineering Materials | Structure and properties of engineering materials, heat treatment, stress-strain diagrams for engineering materials. |
| Metal Casting | Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations. |
| Forming | Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy. |
| Joining | Physics of welding, brazing and soldering; adhesive bonding; design considerations in welding. |
| Machining and Machine Tool Operations | Mechanics of machining, single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, principles of design of jigs and fixtures. |
| Metrology and Inspection | Limits fits and tolerances; linear and angular measurements; comparators; gauge design; inter-ferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly |
| Computer Integrated Manufacturing: | Basic concepts of CAD/CAM and their integration tools |
| Production Planning and Control | Forecasting models, aggregate production planning, scheduling, materials requirement planning. |
| Inventory Control | Deterministic and probabilistic models; safety stock inventory control systems. |
| Operations Research | Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing modes, PERT and CPM. |
