Advanced Mathematical Techniques in Chemical Engineering (CH61015)

This is a core course for M Tech and Dual Degree final year students of Department of Chemical Engineering, IIT Kharagpur. This course has two parts: (i) Linear algebra and (ii) Partial differential equations. I instruct the first part on linear algebra.

Course contents:
- Binary operations; algebraic structures; groups, rings and fields.
- Linear vector spaces; linear independence and linear combinations; basis, dimension and span.
- Analysis of system of equations; null spaces and range spaces.
- Linear transformations; matrices of linear transformations.
- Inner product spaces; normed and metric spaces; adjoint operators.
- Eigenvalue problems, Sturm-Liouville theory.

References:
- Linear Algebra by Gilbert Strang
- Handbook of Linear Algebra by Leslie Hogben (Ed.)
- Theoretical Numerical Analysis by Kendall Atkinson and Weimin Han
- Sturm-Liouville Theory and its Applications by M. A. Al-Gwaiz

Click here to download the course notes and practice problems.

Advanced Thermodynamics (CH62015)

This is a graduate-level 3-1-0 elective. It covers statistical as well as classical chemical thermodynamics.

Course contents:
- Statistical foundations of thermodynamics; degeneracy of microstates; Boltzmann entropy and state of equilibrium; partition function; thermodynamic quantities in terms of the partition function...Notes here...
- Fundamentals of quantum mechanics; wavefunction and its properties; Schroedinger equation and its solution for different potentials; the case of a harmonic oscillator and a two-particle rigid rotator; molecular partition functions...Notes here......Additional reading...
- Kinetic theory of gases; distribution of velocities; theory of diffusion and random walks; energy calculations using classical methods with an overview of molecular simulation techniques...Notes here...
- Thermodynamic potentials and chemical potential; Legendre transformations; partial molar properties and the Gibbs-Duhem equation...Notes here...
- Fugacity and activity; thermodynamic properties of mixtures; ideality and deviation from ideal behaviour in gases and liquids; models for determination of activity coefficients...Notes here...
- Stability of thermodynamic systems; phase equilibria and phase diagrams; supercritical phenomena; Landau theory of phase transitions...Notes here...

References:
- Thermal Physics by Kittel and Kroemer
- The Principles of Statistical Mechanics by Tolman
- Quantum Chemistry by Levine
- Thermodynamics and its Applications by Tester and Modell
- The Principles of Chemical Equilibrium by Denbigh
- Thermodynamics and an Introduction to Thermostatistics by Callen

Process Dynamics and Control (CH61016)

This is a core course for M Tech and Dual Degree final year students of Department of Chemical Engineering, and Dual Degree final year students of Instrumentation specialisation of Department of Electrical Engineering, IIT Kharagpur. This course has two parts: (i) Process dynamics and (ii) Process control. I instruct the first part on process dynamics.

Course contents:
- Analysis of dynamical systems in state-space domain; phase portraits of first order systems; physical examples of linear autonomous first order systems along with the analysis of their dynamical features
- Dynamical analysis of linear higher order autonomous systems; phase protraits; eigenvalue analysis; physical examples and the analysis of dynamical features
- Dynamical analysis of linear non-autonomous systems; multiple input-multiple output systems; similarity transformation; stability analysis; physical examples
- Introduction to non-linear dynamics; different non-linear models for population dynamics; bifurcations in non-linear systems; higher order non-linear systems
- Introduction to discrete-time dynamical systems; conversion of continuous models; fixed point and stability analysis; bifurcation and chaos in discrete-time systems
- Transform domain analysis of dynamical systems; development of first and higher order transfer functions; SISO and MIMO systems and their dynamical analysis; (p,q) order systems; inverse response systems
- Introduction to Z-transforms; relationship between Laplace and Z-transforms; determination of Z- and inverse Z-transforms; application of Z-transforms in the analysis of discrete-time dynamical systems; hold element and pulse transfer function; response and stability of discrete-time systems.

References:
- Process Dynamics, Modeling, Analysis and Simulations by Bequette
- Process Dynamics, Modeling and Control by Ogunnaike and Ray
- Chemical Process Control by Stephanopoulos

Click here to download the course notes.

Quantum Methods in Molecular Simulations (CD61006)

This course witnesses students at all levels from varied departments/centres/schools of the institute. This is a 2-0-3 course involving 2 h of class-room instructions and 3 h of computational lab per week. I co-instruct this course for Centre for Computational and Data Sciences along with my other faculty colleagues from the Department of Chemistry.

Course contents:
- Description of structural features of molecular systems on a computational platform; overview of classical simulation techiques invoking the need of quantum chemical calculations and simulations; basics of statistical mechanics motivating the need to calculate molecular properties.
- Features of energy landscapes for reactive systems; techniques for structural optimisations; Berny and BFGS optimisation algorithms; gradient and Hessian calculations; minimum energy path and transition state calculations; frequency calculations.
- Schroedinger equation; solution of hydrogen atom and visualisation of atomic orbitals.
- Many-body Schroedinger equation; linear combination of atomic orbitals; the concept of basis sets; contracted gaussians and plane wave basis set description; Slater determinant; Hatree-Fock theory

The course is then continued by other colleagues detailing post-HF and DFT methods. The lab involves computational experiments demonstrating the concepts learnt in the theory part and one term project.

References:
- Introduction to Computational Chemistry by Jensen
- Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems by Young
- Exploring Chemistry With Electronic Structure Methods by Foresman

Click here to download the lecture slides.

NPTEL course on Advanced Process Dynamics

NPTEL course on MATLAB-based programming lab