Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors
First order ( linear and non – linear ) equations
higher order linear equations with constant coefficients
Euler – Cauchy equations
Laplace transform and its application in solving linear ODEs
Initial and boundary value problems.
Functions of single variable
Limit, continuity and differentiability
Mean value theorems
local maxima and minima
Taylor and Maclaurin series
Evaluation of definite and indefinite integrals
application of definite integral to obtain area and volume
Partial derivatives
Total derivative
Gradient
Divergence and Curl, Vector identities
Directional derivatives
Line, Surface and Volume integrals
Stokes
Gauss and Green's theorems.
separation of variables
solutions of onedimensional diffusion equation
first and second order one – dimensional wave equation and two-dimensional Laplace equation.
Definitions of probability and sampling theorems
Conditional probability
Discrete Random variables
Poisson and Binomial distributions
Continuous random variables
normal and exponential distributions
Descriptive statistics – Mean, median, mode and standard deviation
Hypothesis testing.
Accuracy and precision
error analysis
Numerical solutions of linear and non – linear algebraic equations
Least square approximation
Newton's and Lagrange polynomials
numerical differentiation
Integration by trapezoidal and Simpson's rule
single and multi – step methods for first order differential equations.
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 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.
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.
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
dehumidification
dehumidification and adsorption.
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.
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.
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.
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 ).