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NUMERICAL ANALSIS [1]

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: 
  1. Calculus of Finite Differences and Numerical Analysis, Gupta and Malik, Krishna Prakashan Mandir
  2. Numerical Methods Problems and Solutions , M.K.Jain, Iyengar,New Age International Ltd.
  3. Numerical Analysis, Sharma & Sharma, Ratan Prakashan Mandir, Agra.
  4. Numerical Mathematical Analysis, Scarborough, James B., Oxford and IBH publishing co.
 
References: 
  1. Applied Numerical Analysis , Gerald, Addison Wesley Publishing Company
  2. Applied Numerical Methods, Gourdin; Boumahrat, Prentice Hall of India
  3. Numerical Methods Problems and Solutions , M.K.Jain, Iyengar,New Age International Ltd
  4. Numerical Analysis a Practical Approach , Melvin J.Maron, Machmillon Publishing Company, New York
  5. Finite differences& Numerical analysis, H.C.Saxena, S.Chand & Co.New Delhi
 
Academic Year: 
2015-2016 [2]

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[1] https://maths.iisuniv.ac.in/courses/subjects/numerical-analsis
[2] https://maths.iisuniv.ac.in/academic-year/2015-2016