Computational Techniques

Paper Code: 
PHY-143 ( B)
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
This course will enable students to:
• Learn computer programming
• Apply softwares like Mathematica/Matlab for solving problems of theoretical Physics 
• Use numerical methods for solving problems in Physics
• Apply quantum simulation techniques for solving problems in physics  
 
12.00
Unit I: 
I
a) A practical approach to learning basic features of operating systems: DOS, UNIX, Windows, Linux; Graphical packages:  Origin, Gnuplot; Latex and Internet.
 
b) C/C++ Programming: Introduction to C/C++, constants, variables, data types, declaration of variables, user defined declaration, operators, hierarchy of arithmetic operators, expressions and statements; control statements: if, switch, conditional operation, go to, if……else; Decision making and looping statements: while, do…while, for built in functions and programme structure, strings; input and output statements; pointers and arrays; sub-programmes; function overloading, recursion; file access.
 
Lab work: 
Solving Problems related to topics covered in the course by actual Programming and obtaining results.
 
12.00
Unit II: 
II
(a) Mathematical Operations using Mathematica (or Matlab): Running Mathematica, numerical calculations, graphics, 3 D plots, equation solving, matrices, mathematical relations, complex numbers, simplifications, algebraic expressions, mathematical operations, in built functions, differentiation, integration, series, limits.
 
(b) Advanced Mathematics:  Procedural programming, loops, conditional programming, producing output, linking external programme, functional programming, numerical operation of data, statistical calculations, minimization, and derivatives of unknown functions. 
 
12.00
Unit III: 
III
(a) Matrices: Product of matrices, inversion using iterative methods and accessory
Numerical Linear Algebra: Solution of system of linear equations, direct methods, error analysis.
Curve fitting: Least square fitting methods, linear regression, polynomial regression, iterative methods.
6 Hrs.
(b) Numerical differentiation and integration methods: Numerical methods for derivatives, minima and maxima of a function, numerical integration methods for one dimensional to multi-dimensional integrations using Simpson’s rule, quadrature formula and Monte Carlo methods.
 
12.00
Unit IV: 
IV
(a) Interpolation: Splines, Numerical methods for ordinary and partial differential equations: Euler’s method, Range-Kutta method for ordinary differential equations; stability and convergence
 
(b) Partial differential equations using matrix method for difference equation, relaxation method, initial value problems, stability, convergence and qualitative properties.
Random numbers, Monte Carlo integral methods, importance of sampling, Fast Fourier Transform.
 
12.00
Unit V: 
V
Quantum Simulations:  Time-independent Schrödinger equation in one dimension (radial or linear equations); Scattering from a spherical potential, Born Approximation. 
 
Bound State Solutions: Single particle time dependent Schrödinger equation; Hartree Fock Theory: restricted and unrestricted theory applied to atoms; Schrödinger equation in a basis: Matrix operations, Variation properties; Application of basis functions to atomic, molecular and solid state calculations. 
 
Essential Readings: 
1. R.S. Salarva: Numerical Methods: A computer oriented approach, (BPB Publ., 1996) 
2. S. Wolfram:  Mathematical, (Addison Wesely)                                                       
3. K. Binder : Application of Monte Carlo Method (Springer Verlog)
4. E. Balaguruswamy: Object Oriented Programming with C++ (Tata Mc Graw Hill, 2000)
5. R.C. Verma: Computer Simulation in Physics (Ananaya Publ. New Delhi, 2004)
6. J.M. Thijssen: Computational Physics (Cambridge University Press, 1999)
7. M.K. Jain, S.R.K. Iyenger and R.K. Jain: Numerical Methods for Scientific and Engineering Computation (Wisely Eastern Ltd.) 
 
References: 
1. V. Rajaraman: Computer based Numerical methods 3rd Ed. Prentice Hall India, 1980) 
2. Bjarne Stroustrup : The C++ Programming Language (Addison Wesely) 
3. V. Rajaraman: Fortran Programming 
4. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. : Numerical Recipes in Votteling C/C++ : The art of Scientific computing (Combridge University Press, 1992)
5. H. Gould and J. Toobochnlik: An introduction to computer simulation methods (Addition Wesely, 1996) 
6. S.E, Koonin and D.C. Meredith : Computational Physics (Addition Wesley, New York, 1990) 
7. B. Chandra : Object oriented Programming using C++ (Narosa, New Delhi, 2002)
8. Harvey Goud and Jain Tobochnik: Computer Simulation Methods (Addoron Wesley Pub. Co. New York, 1988) 
9. S.J. Chapman : Introduction to Fortran 90 and 95 (Mc. Graw Hill, 1998) 
10. Tao Pang: An Introduction to Computational Physics (Cambridge Univ. Press, 1997)
11. R.H. Landon and H.J.P. Mejia: Computational Physics, John Wisely, 1997) 
12. K.H. Hoffmann and H. Schreiber: Computational Physics (Springer, 1996)
13. Steven C. Chopra and Ragwojohd P. Canale: Numerical Methods for Engineers (Mc Graw Hill, New York, 1990) 
14. H.M. Antia: Numerical Methods for Scientists and Engineers
15. D.W. Hermann: Computer Simulation Methods in Theoretical Physics
16. S.S. Sastry: Introductory methods of Numerical Analysis.
17. Aberth Oliver, Precise Numerical Methods using C++.
18. Bjorck A., Numerical Methods for Least Squares. 
19. Collins, G.W.II., Fundamental Numerical Methods and Data Analysis, Case Western Reserve University Internet resource: www.freetechbooks.com/  
fundamental-numerical methods and data-analysis (458:html)
20. Constantinides Alpis and Mostouf Navid, Numerical Methods for Chemical Engineers with MATLAB. 
21. Gerald, Applied Numerical Analysis, Addison Wesley Publishing Company
22. Gourdin, Applied Numerical method, Prentice Hall of India. 
23. Hamming Richard, Numerical Methods for Scientists and Engineers. 
24. Hare, Anthony O, Numerical Methods for Physicists.  http://www.teaching.physics.ox.ac.uk/computing/numericalmethods/NMfP.pdf
25. Kharab and Guenther, An Introduction to Numerical Methods: A-MATLAB Approach. 
26. Saxena H.C., Finite difference and numerical analysis, New Delhi, S Chand & Co.
27. Sharma & Sharma, Numerical analysis, Agra, Ratan Prakashan Mandir. 
 
 
Academic Year: 
2020-2021
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