8 Courses

Department of Computational Sciences

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).

**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

- 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

· 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

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

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

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
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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

**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, CO_{2} 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

**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**