Pcs Patna Summer Assignment 2013 Movies

3,000 get RTE seats in round 1 but schools refuse to start admissions till dues cleared 2018-03-13T19:24:32.086Z

MUMBAI: Over 3,000 students were allotted a school in the city through the first round of lottery held on Tuesday for seats reserved under the Right to Education Act, 2009. Uncertainty, however, looms over their admissions as private schools have decided to boycott the process over non-payment of past dues by the state government. Out of the 10,628 applications received by the BMC, 3,239 were allotted a seat at an unaided non-minority school in round one. Parents of these students can approach the respective schools Wednesday onwards to complete the admission process. A total of 8,374 seats are on offer. “This year, we have reached out to a lot more people and hence, number of applications are higher,” said Mahesh Palkar, education officer, BMC. School associations are, however, determined to continue their protest over pending reimbursements for the past five years. “We have support from most of the schools in the city and none of the admissions will be accepted until the government clears our dues. We have informed them about it ahead of the admission process and they should have not conducted the lottery. The state government is not disclosing the funds they have received from the Centre,” said S C Kedia, secretary, Unaided School Forum. Schools said that they will wait till month-end to hear from the education department. A member of a school management, on condition of anonymity, said, “The government has assured us that reimbursements will be released by March 31, but until then, we won’t accept admissions.” On the other hand, some schools said they will accept all students assigned to them. “We already have over 240 students at our school and we will accept the incoming batch as well. Our management has decided to continue to take in students,” said Madhura Phalke, principal, Pawar Public School, Chandivli. Out of the 347 participating schools, while several received applications much more than their intake capacity, 47 received no applications. Students who do not confirm their admission in this round will not get a chance in the next round. The second round of lottery will be conducted between March 28 and 31.


CH201 GREEN CHEMISTRY AND TECHNOLOGY 3-0-0-6 Pre-requisites:Nil
Principles and Concepts of Green Chemistry: Sustainable development, atom economy, reducing toxicity. Waste: production, problems and prevention, sources of waste, cost of waste, waste minimization technique, waste treatment and recycling. Catalysis and Green Chemistry: Classification of catalysts, heterogeneous catalysts heterogeneous catalysis, biocatalysis. Alternate Solvents: Safer solvents, green solvents, water as solvents, solvent free conditions, ionic liquids, super critical solvents, fluorous biphase solvents. Alternative Energy Source: Energy efficient design, photochemical reactions, microwave assisted reactions, sonochemistry and electrochemistry. Industrial Case Studies: Greening of acetic acid manufacture, Leather manufacture (tanning, fatliquoring), green dyeing, polyethylene, ecofriendly pesticides, paper and pulp industry, pharmaceutical industry. An integrated approach to green chemical industry.

  • V. K. Ahluwalia, Green Chemistry: Environmentally Benign Reactions, Ane Books India, New Delhi, 2006.
  • M. M. Srivastava, R. Sanghi, , Chemistry for Green Environment, Narosa, New Delhi, 2005.


  • 1. P. T. Anastas and J.C. Warner, Green Chemistry, Theory and Practice Oxford, 2000.
  • 2. M. Doble and A. K. Kruthiventi, Green Chemistry and Engineering, Academic Press, Amsterdam, 2007.
  • 3. Mike Lancaster, Green Chemistry: An Introductory Text, Royal Society of Chemistry, 2002.
  • 4. R.E. Sanders, Chemical Process Safety: Learning from Case Histories, Butterworth Heinemann, Boston, 1999.

Algebra and Number Theory

MA212Algebra and Number Theory 3-0-0-6 Pre-requisites:Nil

Algebra: Semigroups, groups, subgroups, normal subgroups, homomorphisms, quotient groups, isomorphisms. Examples: group of integers modulo m, permutation groups, cyclic groups, dihedral groups, matrix groups. Sylow's theorems and applications. Basic properties of rings, units, ideals, homomorphisms, quotient rings, prime and maximal ideals, fields of fractions, Euclidean domains, principal ideal domains and unique factorization domains, polynomial rings. Finite field extensions and roots of polynomials, finite fields.

Number Theory: Divisibility, primes, fundamental theorem of arithmetic. Congruences, solution of congruences, Euler's Theorem, Fermat's Little Theorem, Wilson's Theorem, Chinese remainder theorem, primitive roots and power residues. Quadratic residues, quadratic reciprocity. Diophantine equations, equations ax+by=c, x2+y2=z2, x4+y4=z2 Simple continued fractions: finite, infinite and periodic, approximation to irrational numbers, Hurwitz's theorem, Pell's equation. Partition functions: Formal power series, generating functions and Euler's identity, Euler's theorem, Jacobi's theorem, congruence properties of p(n). Arithmetical functions: Φ(n), μ(n), d(n), σ(n). A particular Dirichlet series for Riemann Zeta Function.

  • I. N. Herstein. Topics in Algebra, Wiley, 2006
  • I. Niven, H.S. Zuckerman, H.L. Montgomery. An introduction to the theory of numbers, Wiley, 2000

  • D.S. Dummit & R.M. Foote. Abstract Algebra, Wiley, 1999
  • G.H. Hardy, E.M. Wright. An introduction to the theory of numbers, OUP, 2008
  • T.M. Apostol. Introduction to Analytic Number Theory, Springer, UTM, 1998


1. Introduction and general notions of point set topology : Open and Closed Sets, Neighbourhoods, Connectedness
and Compactness, Separation, Continuity.
2. An overview of topology and classification of surfaces : Surfaces – orientable and non-orientable, their topology,
classification of closed suraces
3. Combinatorial Techniques : Simplicial complexes, and simplicial maps, triangulations, Euler characteristics, Maps on
4. Homotopy and Homology Groups: Introducing Groups and concept of Homotopy, fundamental group and its
calculations, Homology.
5. Calculating Homology : Computation of homology of closed surfaces.
6. Topics in Geometry : Delauny triangulations, Voronoi diagrams, Morse functions

  • Afra Zomordian: Topology for Computing, CUP, 2005
  • H. Edelsbrunner and J. Harer. Computational Topology. An Introduction. Amer. Math. Soc., Providence, Rhode Island, 2009
  • J. J. Rotman: An introduction to Algebraic Topology, GTM- 119, Springer, 1998


  • Tomasz K., K. Mischaikow and M. Mrozek, Computational Homology, Springer, 2003
  • H.Edelsbrunner, Geometry and Topology for Mesh Generation, CUP, 2001
  • D. Kozlov, Combinatorial Algebraic Topology, Springer, 2008
  • V. A. Vassiliev, Introduction to Topology, AMS, 2001
  • R. Messer and P. Straffin, Topology Now, MAA, 2006



Number Representation and Errors: Numerical Errors; Floating Point Representation; Finite Single and Double Precision Differences; Machine Epsilon; Significant Digits.

Numerical Methods for Solving Nonlinear Equations: Method of Bisection, Secant Method, False Position, Newton‐Raphson's Method, Multidimensional Newton's Method, Fixed Point Method and their convergence.

Numerical Methods for Solving System of Linear Equations: Norms; Condition Numbers, Forward Gaussian Elimination and Backward Substitution; Gauss‐Jordan Elimination; FGE with Partial Pivoting and Row Scaling; LU Decomposition; Iterative Methods: Jacobi, Gauss Siedal; Power method and QR method for Eigen Value and Eigen vector.

Interpolation and Curve Fitting: Introduction to Interpolation; Calculus of Finite Differences; Finite Difference and Divided Difference Tables; Newton‐Gregory Polynomial Form; Lagrange Polynomial Interpolation; Theoretical Errors in Interpolation; Spline Interpolation; Approximation by Least Square Method.

Numerical Differentiation and Integration: Discrete Approximation of Derivatives: Forward, Backward and Central Finite Difference Forms, Numerical Integration, Simple Newton‐Cotes Rules: Trapezoidal and Simpson's (1/3) Rules; Gaussian Quadrature Rules: Gauss‐Legendre, Gauss‐Laguerre, Gauss‐Hermite, Gauss‐Chebychev.

Numerical Solution of ODE & PDE: Euler's Method for Numerical Solution of ODE; Modified Euler's Method; Runge‐Kutta Method (RK2, RK4), Error estimate; Multistep Methods: Predictor‐Corrector method, Adams‐Moulton Method; Boundary Value Problems and Shooting Method; finite difference methods, numerical solutions of elliptic, parabolic, and hyperbolic partial differential equations.

Exposure to software package MATLAB.


  • K. E. Atkinson, Numerical Analysis, John Wiley, Low Price Edition (2004).
  • S. D. Conte and C. de Boor, Elementary Numerical Analysis ‐ An Algorithmic Approach, McGraw‐Hill, 2005.


  • J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd Edition, Texts in Applied Mathematics, Vol. 12, Springer Verlag, 2002.
  • J. D. Hoffman, Numerical Methods for Engineers and Scientists, McGraw‐Hill, 2001.
  • M.K Jain, S.R.K Iyengar and R.K Jain, Numerical methods for scientific and engineering computation (Fourth Edition), New Age International (P) Limited, New Delhi, 2004.
  • S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw‐Hill 2008.


MA251 OPTIMIZATION TECHNIQUES 3-0-0-6 Pre-requisites:Nil

Introduction to linear and non-linear programming. Problem formulation. Geo- metrical aspects of LPP, graphical solution. Linear programming in standard form, simplex, Big M and Two Phase Methods. Revised simplex method, special cases of LP. Duality theory, dual simplex method. Sensitivity analysis of LP problem. Transportation, assignment and traveling salesman problem. Integer programming problems-Branch and bound method, Gomory cutting plane method for all integer and for mixed integer LP. Theory of games: Computational complexity of the Simplex algorithm, Karmarkar's algorithm for LP. Unconstrained Optimization, basic descent methods, conjugate direction and Newton's methods. Acquaintance to Optimization softwares like TORA.

  • Hamdy A. Taha, Operations Research: An Introduction, Eighth edition, PHI, New Delhi (2007).
  • S. Chandra, Jayadeva, Aparna Mehra, Numerical Optimization with Applications, Narosa Publishing House (2009).
  • A. Ravindran, Phillips, Solberg, Operation Research, John Wiley and Sons, New York (2005).
  • M. S. Bazaraa, J. J. Jarvis and H. D. Sherali, Linear Programming and Network Flows, 3rd Edition, Wiley (2004).

  • D. G. Luenberger, Linear and Nonlinear Programming, 2nd Edition, Kluwer, 2003. S. A. Zenios (editor), Financial Optimization, Cambridge University Press (2002).
  • F. S. Hiller, G. J. Lieberman, Introduction to Operations Research, Eighth edition, McGraw Hill (2006).

Optics & Lasers

PH201Optics & Lasers 3-0-0-6 Pre-requisites:Nil

Review of basic optics: Polarization, Reflection and refraction of plane waves. Diffraction: diffraction by circular aperture, Gaussian beams.

Interference: two beam interference-Mach-Zehnder interferometer and multiple beam interference-Fabry-Perot interferometer. Monochromatic aberrations. Fourier optics, Holography. The Einstein coefficients, Spontaneous and stimulated emission, Optical amplification and population inversion. Laser rate equations, three level and four level systems; Optical Resonators: resonator stability; modes of a spherical mirror resonator, mode selection; Q-switching and mode locking in lasers. Properties of laser radiation and some laser systems: Ruby, He-Ne, CO2, Semiconductor lasers. Some important applications of lasers, Fiber optics communication, Lasers in Industry, Lasers in medicine, Lidar.

  • R. S. Longhurst, Geometrical and Physical Optics, 3rd ed., Orient Longman, 1986.
  • E. Hecht, Optics, 4th ed., Pearson Education, 2004.
  • M. Born and E. Wolf, Principles of Optics, 7th ed., Cambridge University Press, 1999.
  • William T. Silfvast, Laser Fundamentals, 2nd ed., Cambridge University Press, 2004.
  • K. Thyagarajan and A. K. Ghatak, Lasers: Theory and Applications, Macmillan, 2008.

Vacuum Science and Techniques

PH203Vacuum Science and Techniques 3-0-0-6 Pre-requisites:Nil

Fundamentals of vacuum, units of pressure measurements, Gas Laws (Boyles, Charles), load-lock chamber pressures, Partial and Vapor Pressures, Gas flow, Mean free path, Conductance, Gauges, Capacitance Manometer, Thermal Gauges, Thermocouple, Pirani Gauge, Penning Gauge, High Vacuum Gauges, Leak Detection, Helium Leak Detection, Cold Cathode Gauge, Roughing (Mechanical) Pumps, Pressure ranges, High Vacuum Pumps: Oil Diffusion Pump, Tolerable fore line pressure System configuration, Oils, Traps Crossover pressure calculations, Pump usage and procedures, Turbomolecular pump, Cryopumps, Pump usages, Out gassing and Leak Testing.

Introduction to Deposition, Anti Reflection (AR) Coatings, Mono-dimensionally modulated (MDM) Filters, Vacuum Coatings, High reflectors, e-Beam deposition systems, Film Stoichiometry, Sputtering, Itching and Lithography, Chemical Vapour deposition and Pulse Laser deposition, Mass Flow control, Reactive sputtering, Film growth control.

  • K.L. Chopra and S.R. Das, Thin Film Solar Cells, Springer, 1983.
  • Nagamitsu Yoshimura, Vacuum Technology: Practice for Scientific Instruments, Springer, 2008.
  • Milton Ohring, Materials Science of Thin Films, Second Edition, Academic Press, 2001.

  • A. Roth, Vacuum Technology, North Holland, 1990.
  • Donald Smith,Thin-Film Deposition: Principles and Practice, McGraw-Hill Professional, 1995.
  • Krishna Shesan, Handbook of Thin Film Deposition, William Andrew, 2002.

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