**Linear Algebra:** Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

**Calculus:** Functions of single variable, Limit, continuity and differentiability, Taylor
series, Mean value theorems, Evaluation of definite and improper integrals, Partial
derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl,
Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes,
Gauss and Green’s theorems.

**Differential equations:** First order equations (linear and nonlinear), Higher order linear
differential equations with constant coefficients, Cauchy’s and Euler’s equations,
Initial and boundary value problems, Laplace transforms, Solutions of one
dimensional heat and wave equations and Laplace equation.

**Complex variables:** Complex number, polar form of complex number, triangle
inequality.

**Probability and Statistics:** Definitions of probability and sampling theorems,
Conditional probability, Mean, median, mode and standard deviation, Random
variables, Poisson, Normal and Binomial distributions, Linear regression analysis.

**Numerical Methods:** Numerical solutions of linear and non-linear algebraic
equations. Integration by trapezoidal and Simpson’s rule. Single and multi-step
methods for numerical solution of differential equations.

**Process Calculations and Thermodynamics:** Steady and unsteady state mass and energy balances including multiphase, multicomponent,
reacting and non-reacting systems. Use of tie components; recycle,
bypass and purge calculations; Gibb’s phase rule and degree of freedom analysis.

First and Second laws of thermodynamics. Applications of first law to close and
open systems. Second law and Entropy. Thermodynamic properties of pure
substances: Equation of State and residual properties, properties of mixtures: partial
molar properties, fugacity, excess properties and activity coefficients; phase
equilibria: predicting VLE of systems; chemical reaction equilibrium.

**Fluid Mechanics and Mechanical Operations:**
Fluid statics, Newtonian and non-Newtonian fluids, shell-balances including
differential form of Bernoulli equation and energy balance, Macroscopic friction
factors, dimensional analysis and similitude, flow through pipeline systems, flow
meters, pumps and compressors, elementary boundary layer theory, flow past
immersed bodies including packed and fluidized beds, Turbulent flow: fluctuating
velocity, universal velocity profile and pressure drop.

Particle size and shape, particle size distribution, size reduction and classification of
solid particles; free and hindered settling; centrifuge and cyclones; thickening and
classification, filtration, agitation and mixing; conveying of solids.

**Heat Transfer:** Steady and unsteady heat conduction, convection and radiation, thermal
boundary layer and heat transfer coefficients, boiling, condensation and
evaporation; types of heat exchangers and evaporators and their process
calculations. Design of double pipe, shell and tube heat exchangers, and single
and multiple effect evaporators.

**Mass Transfer:** Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration
and surface renewal theories; momentum, heat and mass transfer analogies;
stage-wise and continuous contacting and stage efficiencies; HTU & NTU concepts;
design and operation of equipment for distillation, absorption, leaching, liquid-liquid
extraction, drying, humidification, dehumidification and adsorption.

**Chemical Reaction Engineering:** Theories of reaction rates; kinetics of homogeneous reactions, interpretation of
kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors;
residence time distribution, single parameter model; non-isothermal reactors;
kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.

**Instrumentation and Process Control:** Measurement of process variables; sensors, transducers and their dynamics, process
modeling and linearization, transfer functions and dynamic responses of various
systems, systems with inverse response, process reaction curve, controller modes (P,
PI, and PID); control valves; analysis of closed loop systems including stability,
frequency response, controller tuning, cascade and feed forward control.

**Plant Design and Economics:** Principles of process economics and cost estimation including depreciation and
total annualized cost, cost indices, rate of return, payback period, discounted cash
flow, optimization in process design and sizing of chemical engineering equipments
such as compressors, heat exchangers, multistage contactors.

**Chemical Technology:** Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry),
fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper,
Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization
industries (polyethylene, polypropylene, PVC and polyester synthetic fibers).