guidelines for the course

7/18/2019 Guidelines for the Course

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IIT BOMBAY , DEP T. CHEMICAL ENG G.

Mathematical and Statistical Methods in

Chemical Engineering

CL 602 (Aug-Dec 2014)

Instructor: Ratul Dasgupta

Email: [email protected]

TAs

Mr. Palas Farsoiya, Email: [email protected]

Schedule: Tue - Fri (5:05 - 6:30 pm - Room #118)

22nd-July-2014

S YLL AB US

• Linear Algebra - Linear spaces, Vector spaces, Linear operator theory, self-adjoint op-

erators, Eigenvalues and eigenvectors-eigenfunctions, Cayley-Hamilton theorem, Poly-

nomials and functions defined on matrices, Similarity transformations, Jordan forms,

Quadratic forms, Function spaces, Strum-Liouville equations and solution of boundary

value problems, Finite difference equations, Difference operators.

• Partial Differential Equations Partial differential operators, First order partial differen-tial equations, Method of characteristics, Classification of the second order partial dif-

ferential equations and boundary conditions, Method of separation of variables, Simi-

larity solutions, Green’s functions, Laplace and Fourier transforms.

• Nonlinear Ordinary Differential Equations Autonomous/ non-autonomous systems

of odes, Phase plane analysis, Limit cycle and bifurcation, regular and singular pertur-

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bation techniques, Poincare and Liapunov stability criteria, Chaos, Differential-Algebraic

equations.

• Statistical methods: Random variables, Probability distributions, StochasticProcesses,

Random numbers and their generation, Monte-Carlo simulation, Response surface

methodology, First and second order orthogonal factorial design, Regression analysis,

Least square estimation of regression parameters, Lack of fit.

• Graph theory: Classification of graphs, matrix representation of graphs, Analysis of

trees, directed graphs and networks.

TIMELINES

We will spend approximately three-four weeks on every topic.

TEXTBOOKS

For Linear Algebra, I will mainly refer to the two texts below. Occasionally, some material

from elsewhere will also be used. The last text is at an advanced graduate level: should you

attempt reading through it, do this only after you are familiar with the basic ideas from the

course.

• Mathematical Methods in Chemical Engineering - S. Pushpavanam.

• Linear Algebra and its applications - Gilbert Strang.

• Optional Advanced Text:

Mathematics for Physicists - Philippe Dennery and Andre Krezwicki.

For the remainder of the topics, the list of textbooks and references will be provided to you as

we progress.

A SSIGNMENTS AND E XAM S

Each assignment will be published on the course moodle and you will return these to the TA

for evaluation at a pre-assigned date. I would strongly urge you to try all the problems in

the assignments, on your own . During a class immediately after an assignment submission,

a randomly chosen set of people in the class might be asked to come to the board and solve

some of the problems that they have turned in, in their assignments. If you fail to solve theproblem on the board, I will assume that you have not worked out the assignment on your

own. This will lead to penalty. The exams (mid and end) will test your understanding and

originality rather than your ability to remember things.

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GRADING SCHEME

There will be 4 Assignments (30% weight), 2 Quizzes (20% weight) and 2 exams (Mid and

End-Semester with 25% weight on each exam.).

PENALTY FOR LATE SUBMIS SION AND COPYING

You will turn in your assignment to the TA at a preassigned date and time communicated to

you in the class. Late submission will NOT be accepted, unless supported by serious reasons

such as medical certificates. Refrain from approaching me (or the TAs) with imaginary stories

of emergencies justifying late submission(s). You will waste everyone’s time and gain nothing.

A DVISE

Please resist the temptation to copy assignments. An assignment copied from your friend isnot hard to detect. Apart from losing marks1, you also possibly realize that this (inclination to

not do things on your own) slowly destroys your ability to think independently. If you make

this into a habit, you are likely to cause yourself immense scientific harm in the long run.

H AP PY LEARNING!

1The source and the sink will be equally penalized

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