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Numerical Analysis (Code-09050503)

S.No. Topic Domain Hours as per UGC
1 ·         Finite difference operators and their relations Must know 10
·         Finiding the missing terms and effect of error in a difference tabular values
·         Interpolation with equal intervals: Newton’s forward and Newton’s backward interpolation formulae
·         Interpolation with unequal intervals: Newton’s divided difference
·         Lagrange’s interpolation formulae
·         Hermite formula
2 ·         Central Differences: Gauss forward and Gauss’s backward interpolation formulae Must know 15
·         Sterling, Bessel Formula
·         Probability distribution of random variables
·         Binomial distribution
·         Poisson’s distribution
·         Normal distribution: Mean, Variance and Fitting
3 ·         Numerical differentiation: Derivative of a function using interpolation formulae as studied in section-I &II Must know 12
·         Eigen value Problems: Power method, Jacobi’s method
·         Given’s method, House Holder’s method
·         QR method, Lanczos method
4 ·         Numerical integration: Newton’s Cote’s Quadrature formula Must know 14
·         Trapezoidal rule, Simpon’s one-third and three-eigth rule
·         Chebyehev formula, Gauss Quadratic formula
·         Numerical solution of ODEs: Single-step methods-Picard’s method, Taylor’s series method
·         Euler’s method, Runge-Kutta method
·         Multiple step methods, Predictor-corrector metho
·         Modified Euler’s method
·         Milne-Simpson’s method

 

Books Recommended;

  1. Babu Ram: Numerical methods Pearson Publications.
  2. S.Gupta , Elements of Numerical Analysis, Macmillan’s India 2010
  3. K.Jain, S.R.K. Lyengar, R.K. Jain: Numerical methods, Problems ans Solutions, New Age International(P) Ltd., 1996
  4. K.Jain, S.R.K. Lyengar, R.K. Jain: Numerical methods for Scientific and Engineering Computation , New Age International(P) Ltd., 1999
  5. E. Froberg: Introduction to Numerical Analysis (2nd edition )
  6. Y. Rubnistein: Simulation and Monte carlo Methods, John Wiley, 1981.
  7. Melvin J. Marron: Numerical Analysis- A Practical approach ,Macmillan Publishing Co., Inc., New York
  8. Computer Oriented Numerical methods, Printic Hall of India Pvt. Ltd.
  9. Brian bradie, A Friendly : Introduction to of Numerical Analysis Pearsons education India
  10. F. Gerlad and P.O. Wheatley, Applied Numerical Analysis, Pearsons education India.
  11. Uri M. Ascher And Chen. Greif, A First course in Numerical methods, 7th, PHI Learning Private Limited 2013.
  12. John H. Mathews and Kurtis D. Fink, Numerical methods using MATLAB, 4th, PHI Learning Private Limited 2012
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