Utkal University, Odisha, Mathematics Semester 4, Numerical Methods and Scientific Computing Syllabus

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Unit - 1 Rate Of Convergence

Unit 1

Rate of convergence

1.1 Rate of convergence Algorithms

1.2 Errors Relative Absolute Round off Truncation

1.3 Approximations in scientific computing

1.4 Error propagation and amplification conditioning Stability and accuracy

1.5 Computer arithmetic mathematical software and libraries visualization

1.6 Numerical solution of nonlinear equations Bisection method

1.7 RegulaFalsi method Secant method

1.8 Newton Raphson method

1.9 Fixedpoint Iteration method.

Unit - 2 System Of Linear Algebraic Equations

Unit 2

Rate of convergence of the above methods

2.1 Rate of convergence of the above methods

2.2 System of linear algebraic equations Gaussian Elimination and Gauss Jordan methods

2.3 Gauss Jacobi method Gauss Seidel method and their convergence analysis.

2.4 Computing eigenvalues and eigenvectors

Unit - 3 Polynomial Interpolation

Unit 3

Polynomial interpolation

3.1 Polynomial interpolation Existence uniqueness of interpolating polynomials

3.2 Lagrange and Newton’s divided difference interpolation

3.3 Error in interpolation Central difference averaging operators

3.4 Gaussforward and backward difference interpolation

3.5 Hermite and Spline interpolation piecewise polynomial interpolation

Unit - 4 Numerical Integration

Unit 4

Numerical Integration

4.1. Numerical Integration Some simple quadrature rules NewtonCotes rules Trapezoidal rule

4.2 Simpsons rule Simpsons 38th rule

4.3 Numerical differentiation and integration

4.4 Richardson extrapolation

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Other Subjects of Semester-4
Ring theory
Topology of metric spaces
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