CH235: Computer Oriented Numerical Analysis
Introduction
Programming for numerical solutions with highlevel computer languages
(Fortran, C) and mathematical packages (Mathematicaâ
, Matlabâ ). Computer arithmetic and errors.
Types of errors, error estimates and its propagation.
Matrix algebra
Definitions. Basic properties and operations. Numerical evaluation of
the norm, condition number, rank and determinant of a matrix. Methods to
solve banded and sparse matrices.
Linear algebraic equations
Solutions of systems of algebraic equations, existence and uniqueness
of solutions. Numerical evaluation using Cramer’s rule, Gauss elimination
with and without pivoting, LU decomposition, Cholesky factorization and
GaussJordan technique. Iterative techniques using the methods of Jacobi,
GaussSeidel and overrelaxation. Convergence criteria and error estimation.
Eigenvalues and eigenvectors
Definition and properties. Numerical evaluation using FaddeevLeverrier
technique, power, inverse power and modified power methods. Application
of Householder, Rutihauser LU and QR algorithms.
Nonlinear polynomial equations
Numerical solutions using fixed point iteration method, Aitken acceleration,
NewtonRaphson, regula falsi and BirgeVieta. Methods for initial approximation
and determination of complex roots with the methods of Lin and Baristow.
Function approximation
Linear regression. Interpolation using Newton’s forward, backward, divided
differences. Properties, uses and types of interpolating polynomials like
Bessel, Stirling and Lagrangian. Interpolation with periodic and nonperiodic
cubic splines and polynomial approximation of surfaces. Chebyshev polynomials
and Pade’s approximation with rational functions.
Numerical integration and differentiation
Application of trapezoidal, Simpson, midpoint, Romberg and MonteCarlo
techniques. Adaptive integration and multiple integrals. Gaussian Quadrature.
Numerical differentiation and derivatives of interpolating polynomials.
Ordinary differential equations
Initial value problems. Numerical solutions using AdamsBashforth,
AdamsMoulton, Euler and modified Euler methods. Application of RungeKutta
methods and predictorcorrector techniques. Stability and convergence criteria,
stepsize control and error estimation. Higher order equations and systems
of equations. Solutions of equations coupled with algebraic equations.
Stiffness and Gear’s technique for stiff equations.
Boundary value problems. Shooting method. Solving characteristic
value problems and problems with derivative boundary conditions.
Formulation and application of finite differences. Application of orthogonal
collocation and orthogonal collocation on finite elements for sharp gradients.
Solutions with the RayleighRitz method.
Partial differential equations
Solutions of parabolic, hyperbolic and elliptic equations. Representation
as a difference equation. Solution using the explicit, ADI and CrankNicholson
techniques. Numerical stability and convergence criteria. Solving complex
grids and irregular boundaries. Application of OC and OCFE techniques.
Application of the Galerkin finite element method.
References
 Chapra, S.C. and Canale, R.P., Numerical Methods for Engineers, McGraw Hill, NY, 6th edition (2010).
 Gupta, S.K., Numerical methods for Engineers, New Age Publishers, India (2009).
 K.J. Beers, Numerical Methods for Chemical Engineering, Cambridge Univ. Press, Cambridge, UK (2010).
Course Policies
Grading
Two exams  40%
Assignments  10%
Final exam  50%
All exams will be open notes. The final grades
will be based on the total marks obtained relative to the class average.
Assignments
Assignments are an essential part of the learning
process, especially in computational courses. All assignments will involve
working with a computer using Fortran/C and Mathematica/Matlab. You will
be required to submit assignments on time at regular
intervals.
 CH 236: Separation Processes
Types of separation processes.
Thermodynamics of separation
processes: Nonideal property models and activity coefficient
models.
Single equilibrium stages and
flash
calculations: Multicomponent bubble and dew point calculations.
Multicomponent Liquid  liquid, Solid  liquid, Gas  liquid, Gas 
solid and
multiphase systems.
Cascades: Configurations.
Solidliquid, liquidliquid and vaporliquid cascades.
Distillation of Binary systems.
LLE
of ternary systems.
Methods for Multicomponent,
multistage absorption, stripping, distillation and extraction : FUG,
Equationtearing, InsideOut, Mesh methods.
Enhanced distillation:
Extractive,
Salt, Reactive, Pressure  swing.
Supercritical extraction: Theory
and
applications.
Adsorption: Sorbents,
equilibrium,
kinetics and transport considerations. Modeling adsorption
breakthroughs
and desorption profiles. Types of adsorption including pressureswing,
thermal swing and slurry.
Chromatography: Theory and
applications.
Crystallization: Theory,
population
balance models and crystal size distributions.
Course Policies
The
course assumes the
student has a good knowledge of thermodynamics, mass transfer and
numerical methods.
Grading
Two exams  30%
Projects  20%
Final exam  50%
The two exams are open notes and
will be held from 911 am on the third or fourth Saturday of February
and
March. The final exam will be a combination of closed notes (10%) and
open
notes (40%). The final grades will be based on the total marks obtained
relative
to the class average. The projects will be entirely based on the usage
of ASPEN PLUS* to solve various problems.
<> *ASPEN is a
processsimulation software package that is widely used in industry. Given a conceptual process design, ASPEN uses
mathematical models of process equipment and physical/thermodynamic
properties
to predict the performance of the process. This information can then be
used in
an iterative fashion to optimize the design. ASPEN can handle very
complex processes,
including multiplecolumn separation systems, chemical reactors,
distillation
of a chemically reactive compounds, and even electrolyte solutions
like
mineral acids and sodium hydroxide solutions.
It should be emphasized that ASPEN does not design
the process. It takes a design
that the user supplies and simulates the
performance of the process specified in that design. A solid
understanding
of the underlying chemical engineering principles is needed to supply
reasonable values of the input parameters and to evaluate the
suitability of
the predicted results. For instance, a user should have some idea of
process
equipment behavior before attempting to use ASPEN.
Our
goal in using ASPEN is to become familiar
with its basic operation and to perform several
material and energy balance calculations. Subsequently,
you will use the full capability of ASPEN in
simulating processes.
 CH 237: Polymer Engineering and Science
Types of polymerization processes.
Definitions; polymer, plastic, rubber, thermoplastic, thermoset, composite, glass transition; Size of polymers in solution and the molten state; number and weight average molecular masses, distribution of mass, polydispersity index; concepts of amorphous and crystalline polymers.
Addition polymerisation; examples of addition polymers. kinetics of chain growth polymerisation; radical polymerisation, general concepts; initiation of radical polymerisation, types of initiation, chemistry of initiation, kinetics of initiation; initiator half lives; propagation of radical polymerisation.
Chemistry of propagation in radical polymerisation; termination in radical polymerisation, chemistry and kinetics, rate of radical polymerisation; chain transfer in radical polymerisation; kinetic chain length; molecular mass of radical polymerisation; chain transfer coefficients. Step growth/condensation polymerisation; examples of condensation polymers, general considerations for step growth polymerisation.
Brief introduction to ionic polymerisation; process considerations in anionic polymerisation; concept of living polymerisation; PDI in anionic polymerisation.
Molecular masses of condensation polymers; effects of non stoichiometry; extent of reaction, Carothers equation; calculating Mn and Mw from extent of reaction; FlorySchulz distributions; kinetics of step growth
Further examples of condensation polymers; consideration of the effects of side reactions in synthesis; biodegradable polymers Copolymerization; types of copolymers; copolymer equation; reactivity ratios; determination of reactivity ratios; KelenTudos; MayoLewis. Isomerism; sequence isomerism; stereoisomerism; bond structure; conformation; random walks. Crystallization of polymers: Theory, population balance models and crystal size distributions. XRD; Flory model Characterisation of polymers; solution viscometry; Lattice model; regular solution theory; Mark Houwink equation and constants; viscosity equations; FloryFox equation; hydrodynamic volumes, Factors affecting Tg; Phase behavior;
Determination of molecular weight; Viscosity based methods; Light scattering techniques; Gel permeation chromatography/ Size exclusion chromatography;: Theory and
applications. Mechanical properties; Maxwell mode; Voigt model; Elasticity theories; Rubber elasticity. Chemistry and applications of commercial plastics; polymer processing extrusion, calendering, injection and compression moulding  engineering basis and applications
Course Policies
The course assumes the
student has a good knowledge of chemistry and mathematics at the preuniversity level.
Grading
Two exams  50%
Final exam  50%
The two exams are open notes and
will be held from 911 am on the second or third Saturday of September and October. The final exam will be a combination of closed notes and open
notes. The final grades will be based on the total marks obtained relative
to the class average.
In addition, each student will be required to submit a term paper near the end of the semester. A list of possible topics for the paper are in the syllabus; other topics are highly encouraged. The paper should be about 10 pages of double spaced text, but fewer pages will be happily accepted as long as the paper has sufficient content. The paper will be graded as to 1) understanding of the topic (25%), 2) depth of search (25%, go narrow and deep, not wide and broad, for wide is the gate and broad is the way that leadeth to low scores), 3) critical analysis or engineering analysis (25%), and 4) report presentation (25%, grammar, length, neatness, etc.).

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