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Course Co-ordinated by IIT Roorkee
Coordinators
 
Prof. Roshan Lal
IIT Roorkee

 
Dr. Sandip Banerjee
IIT Roorkee

 

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  1. Errors Analysis.

  2. System of Linear Equations.

  3. Eigen values and Eigen vectors

  4. Roots of Non-linear Equations.

  5. Finite Differences and Divided Differences.

  6. Interpolation.

  7. Numerical Differentiation.

  8. Numerical Integration.

  9. Numerical Solution of ODE.

Module

Topics and Contents

Lectures

1

Error Analysis

Types of errors, Propagation of errors, Correct and Significant digits, Examples and exercises.

3

2

Solution of System of Linear Equations

Exact methods: LU-decomposition, Gauss-elimination methods without and with partial pivoting. Iterative methods: Gauss-Jacobi and Gauss-Seidal methods, Matrix norm, Condition number and Ill-conditioning, Examples and Exercises.

4

3

Eigen values and Eigen vectors

Largest and Smallest eigen values and eigen vectors by power method, Examples and Exercises.

8

4

Roots of Non-linear Equations

Bisection, Regula Falsi, Newton–Raphson methods, Direct Iterative method with convergence criterion, Extension of Newton-Raphson and Iterative methods for two variables, Examples and Exercises.

7

5

Finite Differences and Divided Differences

Operators, Difference table, Propagation of errors, Divided differences with properties, Examples and Exercises.

4

6

Interpolation

Interpolation Formulae: Newton’s forward, backward, Stirling’s and Bessel’s  formulae,  Newton’s divided difference and Lagrange’s formulae, Errors in various interpolation formulae. Inverse Interpolation: Successive approximation and Lagrange’s method, Examples and Exercises.

4

7

Numerical Differentiation

Various formulae for first and second derivative with errors, Examples and Exercises.

4

8

Numerical Integration

Newton-Cotes formulae, General quadrature formula for equidistant ordinates, Trapezoidal, Simpson’s 1/3 and 3/8 rules with their geometrical interpretations and errors, Romberg integration and Gaussian quadrature formulae, Examples and Exercises.

4

9

Numerical solution of ODE

Picard, Taylor series, Modified-Euler, Fourth order Runge-Kutta methods with errors, Examples and Exercises.

5

  • James Scarborough, Numerical Mathematical Analysis, Oxford & IBH Publishing Co. Pvt. Ltd (1950), ISBN 10: 0009780021, ISBN-13:978-0009780021.

  • M. K. Jain, SRK Iyengar and R.K. Jain, Numerical Methods For Scientific & Engg 5e, New Age International (P) Ltd (2008), ISBN-13:978-8122420012.

  • C.F. Gerald and O.P. Wheatley, Applied Numerical Analysis, Addison Wesley; 7 edition (2003) , ISBN-13:978-0321133045.



  • Kendall E. Atkinson, An Introduction to Numerical Analysis, Wiley; 2 edition, (January 17, 1989), ISBN-10: 0471624896 , ISBN-13: 978-0471624899.

  • S.S. Sastry, Introductory Methods Of Numerical Analysis, Prentice Hall of India Pvt. Ltd. (2007), ISBN-13: 978-8120327610.

  • B.S. Grewal, Numerical Methods In Engineering & Science With Programs In Fortran 77, C & C++,  Khanna Publishers (2008), ISBN-13: 978-8174091468.



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