Department of Computational Sciences

Classical Mechanics (PCP.507)

The overall goal of this course is to provide tools and applications of classical mechanics that student can use these in various branches of physics. Students who have completed this course have a deep understanding of solid understanding of classical mechanics (Newton’s laws, Lagrangian mechanics, conservation principles, Hamiltonian formalism, Hamilton - Jacobi theory, central force, scattering, rigid body dynamics, small oscillations and special relativity). Establish firm physics and math foundation on which student can build a good carrier in physics.

Course Content

Unit-I                                                                                                                                                         16 hours

Lagrangian Formalism: Newton’s laws, Classification of constraints, D’Alembert’s principle and its applications, Generalized coordinates, Lagrange’s equation for conservative, non-conservative and dissipative systems and problems, Lagrangian for a charged particle moving in an electromagnetic field, Cyclic-coordinates, Symmetry, Conservations laws (Invariance and Noether’s theorem).                          

Hamiltonian Formalism: Variational principle, Principle of least action, Hamilton’s principle, Hamilton’s equation of motion, Lagrange and Hamilton equations of motion  from Hamilton’s principle, Hamilton’s principle to non-conservative and non-holonomic systems, Dynamical systems, Phase space dynamics and stability analysis. 

Unit-II                                                                                                                                                       14 hours

Canonical Transformations and Hamilton - Jacobi theory: Canonical transformation and problems, Poisson brackets, Canonical equations in terms of Poisson bracket, Integral invariants of Poincare, Infinitesimal canonical transformation and generators of symmetry, Relation between infinitesimal transformation and Poisson bracket, Hamilton–Jacobi equation for Hamilton’s principal function, Linear harmonic oscillator problem by Hamilton-Jacobi method, Action angle variables, Application to Kepler’s problem.

 

Unit-III                                                                                                                                             15 hours

Rigid Body Dynamics: Euler’s angles, Euler’s theorem, Moment of inertia tensor, Non- inertial frames and pseudo forces: Coriolis force, Foucault’s pendulum, Formal properties of the transformation matrix, Angular velocity and momentum, Equations of motion for a rigid body, Torque free motion of a rigid body - Poinsot solutions, Motion of a symmetrical top under the action of gravity.    

Two Body Problems: Central force motions, Reduction to the equivalent one-body problem, Differential equation for the orbit, Condition for closed orbits (Bertrand’s theorem), Virial theorem, Kepler’s laws and their derivations, Classification of orbits, Two body collisions, Scattering in laboratory and centre-of-mass frames.

 

Unit-IV                                                                                                                                         15 hours

Theory of Small Oscillations: Periodic motion, Types of equilibria, General formulation of the problem, Lagrange’s equations of motion for small oscillations, Normal modes, Applications to linear triatomic molecule, Double pendulum and N-Coupled oscillators.

Special Theory of Relativity: Lorentz transformations and its consequences, Relativistic kinematics and mass energy equivalence, Relativistic Lagrangian and Hamiltonian, Four vectors, Covariant formulation of Lagrangian and Hamiltonian.

      

Department of Computational Sciences

Mathematics for Computational Sciences (PCP.506)

• Identify and describe the basic mathematical techniques that are commonly used by chemist.
• Develop skills in vectors, matrices, differential calculus, integral calculus and probability.
• Apply the principles to a number of simple problems that have analytical solutions.

Course Content

 

Unit I                                                                                       15 Hours                                 

Matrices & Vector Calculus: matrix algebra, Caley-Hamilton theorem, Eigen values and Eigen vectors, curvilinear coordinates. (Vector calculus: properties of Gradient, divergence and Curl, spherical and cylindrical coordinates)

Differential calculus: Functions, continuity and differentiability, rules for differentiation, applications of differential calculus including maxima and minima, exact and inexact differentials with their applications to thermodynamic properties.

 

Unit II:                                                                                      15 Hours

Integral calculus: basic rules for integration, integration by parts, partial fraction and substitution, reduction formulae, applications of integral calculus, functions of several variables, partial differentiation, co-ordinate transformations

Fourier Transforms: Fourier series, Dirichlet condition, General properties of Fourier series, Fourier transforms, their properties and applications,

 

Unit III:                                                                                   14 Hours

Delta, Gamma, and Beta Functions: Dirac delta function, Properties of delta function, Gamma function, Properties of Gamma and Beta functions.

Special Functions: Legendre, Bessel, Hermite and Laguerre functions, recurrence relations, Orthogonality and special properties. Associated Legendre functions: recurrence relations, Parity and orthogonality, functions, Green’s function,

 

Unit IV:                                                                                   16 Hours

Differential Equations Solutions of Hermite, Legendre, Bessel and Laugerre Differential equations, basics properties of their polynomials, and associated Legendre polynomials, Partial differential equations (Laplace, wave and heat equation in two and three dimensions), Boundary value problems and Euler equation.

Department of Computational Sciences

Molecular Spectroscopy (CCC.557)

·      Gain the knowledge about various spectroscopic techniques, such as, electronic, microwave, vibrational, raman, nuclear magnetic resonance, and laser spectroscopy

·      Understand, how spectroscopic transitions come into picture in molecular quantum mechanics

·      Learn various spectroscopic selection rules and their applications

Department of Computational Sciences

Computational Genomics and Proteomics

Unit I 7 Hours The Importance of DNA-Protein Interactions During Transcription. Initiation-Regulation of Transcription, Synthesis and Processing of the Proteome, The Role of tRNA in Protein Synthesis, The Role of the Ribosome in Protein Synthesis, Post-translational Processing of Proteins, Protein Degradation. Unit 2 8 Hours Role of bioinformatics-OMIM database, integrated genomic maps, gene expression profiling; identification of SNPs, SNP database (DbSNP) Unit 3 8 Hours DNA microarray: database and basic tools, Gene Expression Omnibus (GEO), ArrayExpress, SAGE databases, understanding of microarray data, normalizing microarray data, detecting differential gene expression, Unit 4 7 Hours Only for yeasts: building predictive models of transcriptional regulatory networks using probabilistic modeling techniques.

Department of Computational Sciences

Sequence Analysis

Unit 1 13 Hours

 Basic concepts of sequence similarity, identity and homology, homologues, orthologues, paralogues and xenologues Pairwise sequence alignments: basic concepts of sequence alignment, Needleman and Wunsch, Smith and Waterman algorithms for pairwise alignments, gap penalties 

Unit 2 10 Hours 

Scoring matrices: basic concept of a scoring matrix, PAM and BLOSUM series Tools such as BLAST (various versions of it) and FASTA 

Unit 3 12 Hours Multiple sequence alignments (MSA): basic concepts of various approaches for MSA (e.g. progressive, hierarchical etc.). Algorithm of CLUSTALW (including interpretation of results), concept of dendrogram and its interpretation. 

Unit 4 10 Hours Sequence patterns and profiles: Basic concept and definition of sequence patterns, motifs and profiles, profile-based database searches using PSIBLAST, analysis and interpretation of profile-based searches.

Department of Computational Sciences

Concepts of Genetics

Unit 1 8 Hours Introduction and scope of genetics, DNA as genetic material: Double helical structure, Structure of DNA and RNA, Different types of DNA molecules, forces stabilizing nucleic acid structure, super coiled DNA, properties of DNA, denaturation and renaturation of DNA and Cot curves. DNA replication: Basic mechanism of DNA replication. Unit 2 7 Hours Cell division and Cell cycle: Mitosis, Meiosis Concepts of Linkage analysis and gene mapping: Coupling and repulsion phase linkage, Crossing over and recombination. Population genetics: Application of Mendel’s laws to L T P Cr 2 0 0 2 8 populations, Hardy-Weinberg principle, inbreeding depression and heterosis, inheritance of quantitative traits. Unit 3 7 Hours Gene Interaction: Sex determination and Sex linked inheritance, Sex determination in humans, Drosophila and other animals, Sex determination in plants, Sex linked genes and dosage compensation. Unit 4 8 Hours Chloroplast and Mitochondrial inheritance, Yeast, Chlamydomonas/Neurospora Chromosomal aberrations: Types of changes– deletions, duplications, inversions, translocations, Change in chromosome number: trisomy and polyploidy.

Department of Computational Sciences

Physical Chemistry I

Unit 1                                                                                     9 Hours

Thermodynamics: Thermodynamic functions and their applications, thermodynamic processes, Concepts involved in first, second and third law of thermodynamic, Maxwell relations, Helmholtz and Gibbs Energies, Law of Mass Action, equilibrium constant, Le-Chatlier Principle, temperature-dependence of equilibrium constant and Van't Hoff equation.

 

Unit 2                                                                                    10 Hours

Partial Molar Properties and Fugacity: Partial molar properties. Chemical potential of a perfect gas, dependence of chemical potential on temperature and pressure, Gibbs- Duhem equation, real gases, fugacity, its importance and determination, standard state for gases.

Phase transition: Phase rule, water, CO₂ phase transition, binary and ternary component phase transitions. Clausius-Clapeyron equation and its application to solid-liquid, liquid-vapour and solid-vapour equilibria.

 

Unit 3                                                                                    13 Hours

Thermodynamics of Simple Mixtures: Thermodynamic functions for mixing of perfect gases. chemical potential of liquids. Raoult’s law, thermodynamic functions for mixing of liquids (ideal solutions only). Real solutions and activities.

Solid-Liquid Solutions: Solutions of nonelectrolytes and electrolytes. Colligative properties of solutions, such as osmotic pressure, depression of the freezing point and elevation of the boiling point.

 

Unit 4                                                                                   13 Hours

Statistical Thermodynamics: Thermodynamic probability and entropy, Maxwell-Boltzmann, Bose-Einstein and Dermi-Dirac statistics. partition function, molar partition function, thermodynamic properties in term of molecular partition function for diatomic molecules, monoatomic gases, rotational, translational, vibrational and electronic partition functions for diatomic molecules, calculation of equilibrium constants in term of partition function. monoatomic solids, theories of specific heat for solids.

Department of Computational Sciences

Basics of Biochemistry

Unit 1                                                                                     8 Hours

Principles of biophysical chemistry Thermodynamics, Colligative properties, Stabilizing interactions: Van der Waals, Electrostatic, Hydrogen bonding, Hydrophobic interaction, etc.

 

Unit 2                                                                                     6 Hours

Composition, structure, function and metabolism of Carbohydrates, Lipids.

 

Unit 3                                                                                     6 Hours

Composition, structure, function and metabolism of Amino Acids and Nucleotides.

 

Unit 4                                                                                     8 Hours

Enzymology: Classification, Principles of catalysis, Mechanism of enzyme catalysis, Enzyme kinetics, Enzyme regulation, Isozymes.