Course Co-ordinated by IIT Roorkee
 Coordinators IIT Roorkee IIT Roorkee

Untitled Document
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
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