NUMERICAL ANALSIS
Paper Code:
MAT402
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Unit I:
I
9.00
Differences, Relation between differences and derivatives,difference of polynomials, Factorial notation,Newton’s forward and backward interpolation formula (including proof) .
Unit II:
II
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.
Unit III:
III
9.00
Numerical integration – Quadrature formula-trapezoidal rule, Simpson’s 1/3 rd and 3/8 th formulae,Gaussian Integration , Newton cotes formula.
Unit IV:
IV
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
Unit V:
V
9.00
Solution of system of linear equations: Gauss elimination method , Jacobi and Gauss Seidal method . Solutitons of ordinary differential equations with initial boundary conditions: Picard’s method, Euler’s and modified Euler’s method, Runge’s Kutta Method.
Essential Readings:
- Calculus of Finite Differences and Numerical Analysis, Gupta and Malik, Krishna Prakashan Mandir
- Numerical Methods Problems and Solutions , M.K.Jain, Iyengar,New Age International Ltd.
- Numerical Analysis, Sharma & Sharma, Ratan Prakashan Mandir, Agra.
- Numerical Mathematical Analysis, Scarborough, James B., Oxford and IBH publishing co.
References:
- Applied Numerical Analysis , Gerald, Addison Wesley Publishing Company
- Applied Numerical Methods, Gourdin; Boumahrat, Prentice Hall of India
- Numerical Methods Problems and Solutions , M.K.Jain, Iyengar,New Age International Ltd
- Numerical Analysis a Practical Approach , Melvin J.Maron, Machmillon Publishing Company, New York
- Finite differences& Numerical analysis, H.C.Saxena, S.Chand & Co.New Delhi
Academic Year:
