MCA – II SEMESTER
MCA 110 NUMERICAL ANALYSIS AND OPTIMIZATION
TECHNIQUES
| L | T | P | Total | Credits-4 |
| 4 | 0 | 0 | 4 | Duration of Exam- Three hours |
Errors in numerical calculations, sources of errors, significant digits, numerical solution of polynomial and transcendental equations, bisection method, regula-falsi method, Newton-Raphson method, fixed point method of iteration, rates of convergence of these methods, solution of system of algebraic equations, exact methods, Crout’s triangularization method, iterative methods, gauss – seidel and relaxation method, polynomial interpolation, Lagrange interpolation polynomial, divided differences, Newton’s divided difference interpolation polynomial, finite differences, operators ,∇,E,δ, Gregory, Newton forward and backward difference interpolation polynomials, central differences, stirlings interpolation formulae.
Numerical differentiation, differentiation formulae in the case of equally spaced points, numerical integration, trapezoidal and Simpson’s rules, compounded rules, errors of interpolation and integration formulae numerical solution of ordinary differential equations, single stepmethods, Taylor series method, Euler’s method, modified Euler’s method, Picard’s iteration method, Runge – Kutta methods (2nd, 3rd and 4th order formulae- derivations not required), multistep methods, Milne’s predictor and corrector formulae
Optimization methods, mathematical formulation of linear programming problem, simplex method, artificial variables, Charnes M method, two phase technique, duality in linear programming, dual simplex method, Transportation assignment and routing problems
Suggested References
- Sastry S. S., Numerical Analysis, Prentice-Hall India.
- S. S. Rao, Optimization Techniques, New Age Int., New Delhi
- Froberg, Introduction to Numerical Analysis, Second Edition, Addition Wesley
- Grawin W.W., Introduction to Linear Programming, McGraw Hill
DEPARTMENT OF COMPUTER APPLICATIONS, NIT Kurukshetra