Numerical Analysis

Syllabus Details

• Unit I:(Nonlinear Equations) Numerical solution of non-linear equations: Bisection method, Fixed point iteration, Newton-Raphson method, Secant method, Rate of convergence and error analysis.
• Unit II:(Linear Systems) Direct and Iterative methods for solving systems of linear equations: Gauss elimination, LU decomposition, Jacobi method, Gauss-Seidel method, Convergence analysis.
• Unit III:(Interpolation and Approximation) Polynomial interpolation: Lagrange interpolation, Newton’s divided difference interpolation, Error of interpolation, Hermite interpolation, Spline interpolation.
• Unit IV:(Numerical Calculus) Numerical Differentiation and Integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rules, Gauss quadrature formulas, Error estimation.
• Unit V:(Differential Equations) Numerical solution of ordinary differential equations: Euler’s method, Modified Euler’s method, Runge-Kutta methods, Stability and error analysis.

Course Learning Objective

1. Apply appropriate algorithms to solve selected problems manually.
2. Compare different algorithms with respect to accuracy and efficiency of solution.
3. Analyze the errors obtained in the numerical solution of problems.
4. Use appropriate numerical methods to determine the solutions to given non-linear equations.
5. Use appropriate numerical methods to determine approximate solutions to systems of linear equations.

Recommended Books

1. Atkinson, K. E. An Introduction to Numerical Analysis. 2nd ed. John Wiley & Sons, 1989
2. Burden, R. L. and Faires, J. D. Numerical Analysis. 9th ed. Brooks/Cole, Cengage Learning, 2010
3. Jain, M. K., Iyengar, S. R. K. and Jain, R. K. Numerical Methods for Scientific and Engineering Computation. 6th ed. New Age International Publishers, 2012
4. Conte, S. D. and de Boor, C. Elementary Numerical Analysis: An Algorithmic Approach. 3rd ed. McGraw-Hill, 1980