Numerical Analysis
Paper Code:
MAT402
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Objective:
o To understand the subject as tool applicable in other branches of Sciences, Engineering and Technology.
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 Int. Ltd.
- Numerical Analysis, Sharma & Sharma, Ratan Prakashan Mandir, Agra.
- Numerical Analysis, Bansal, Bhargava, Agarwal, JPH, Jaipur.
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.
- Introductory Methods of Numerical Analysis, S.S. Sastry, Prentice Hall of India.
Academic Year:
