Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and Eigen vectors
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems
First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, Solution integrals.
Probability and Statistics:
Sampling theorems, Conditional probability, Mean, Median, Mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Solutions of non-linear algebraic equations, Single and multi-step methods for differential equations,
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, 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; radioactive heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods, Thermodynamics: Zeros, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle, irreversibility and availability; behavior 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, Rankin, Braxton 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 Braytoncycle; moist air: psychometric chart, basic psychometric processes,Turbomachinery: Pelton-wheel, 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