NUMERICAL ANALYSIS

Paper Code: 
MAT402
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
9.00

Differences, Relation between differences and derivatives, Difference of polynomials, Factorial notation, Newton’s forward and backward interpolation formula (with proof).

9.00

Divided differences: Newton’s and Lagrange’s divided differences formulae. Central differences: Gauss’s, Stirling’s and Bessel’s interpolation formulae, Numerical differentiation. 

9.00

Numerical integration: Newton-Cotes quadrature formula, Trapezoidal formula, Simpson’s 1/3rd and 3/8th formulae, Gaussian integration.

9.00

Inverse Interpolation, Numerical solution of algebraic and transcendental equations: Bisection method, Regula-falsi method, Method of iteration and Newton Raphson’s Method, Newton’s iterative formula for obtaining square and inverse square root.

9.00

Solution of system of linear equations: Direct method (Gauss elimination method, LU- decomposition method), Iterative methods (Jacobi and Gauss Seidal method, SOR method), Theorems based on iterative methods, Solutions of first order  ordinary differential equations: Picard’s method, Euler’s method, Runge-Kutta method.

Essential Readings: 
  1. J.L. Bansal, J.P.N. Ojha, Numerical Analysis, Jaipur publishing house, 2015.
  2. M.C. Goyal, D.C. Sharma, Kavita Jain, Numerical Analysis, RBD, 2015.
  3. M.K. Jain, Iyengar, Numerical Methods Problems and Solutions, New Age International Ltd., 2007.
  4. James B. Scarborough, Numerical Mathematical Analysis, Oxford and IBH publishing 1966.
  5. J.P. Chauhan, Numerical Analysis, Krishna Prakashan Meerut, 2014.
References: 
  1. Curtis F. Gerald, Patrick O. Wheatley Applied Numerical Analysis, Pearson, 2003.
  2. Gourdin, Boumahrat , Applied Numerical Methods,  Prentice Hall of India,1996.
  3. Melvin J.Maron, Robert J.Lopez , Numerical Analysis a Practical Approach, Machmillon Publishing Company, New York, 3rd Edition ,1991.
  4. H. C. Saxena, Finite differences & Numerical analysis, S.Chand & Co. New Delhi, 2010.
  5.  B.S. Goel, S.K. Mittal, Numerical Analysis, Pragati Prakashan, Meerut, 2007.
  6. Walter Gautschi, Numerical Analysis, Birkhauser Springer US, 2012.

(Note: Non-Programmable scientific calculator up to 100 MS is permitted)

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