FACULTY MEMBER :
DEPARTMENT OF MATHEMATICS
To provide the idea of various computational methods; concepts, which have close application to the guide.
1. NON-LINEAR EQUATIONS:
Solving non linear equations-Regula Falsi method-Newton's method-order of convergence-Graeffe's method and Bairstow's methodincluding the case of pairs of complex roots-Newton's method for f(x,y)=0,g(x,y)=0.
2. LINEAR SYSTEMS:
Solution of linear equations-Gaussian elimination,Gauss Jordan and Crout's methods-Finding the inverse of a matrix using elementary row transformations-Gauss Seidel and Jacobi iterative methods-Power method to find dominant eigen value and eigen vector.
3. INTERPOLATION AND CURVE FITTING:
Newton's forward and backward interpolation-Lagrange's interpolation-Newton's divided difference method-cubic spline interpolation-natural splines-choosing appropriate curve and fitting to data-curve fitting-Method of least Squares-regression equations.
4. NUMERICAL SOLUTION OF ODE(Ordinary Differential Equation):
Euler's method-Euler's modified method-Taylor's method - Runge-Kutta method of second and fourth order-Simultaneous equations and higher order equations by Taylor's method and Runge-Kutta method-Multistep method-Milne's and Adams' predictor-corrector methods.
5. NUMERICAL SOLUTION OF PDE(Partial Differential Equation):
Boundary value problems - finite difference methods - second order linear PDEs - solution of Laplace and Poisson equation by Liebmann's method - solution of one Dimensional heat flow and wave equations.
1. M. K. Venkataraman, "Numerical Methods in Science and Engineering" NPC 2nd Edn.,(For Unit I)1986.
2. M.K.Jain, SRK lyengar and R.K.Jain, "Numerical Methods for Scientific and Engineering Computation", Wiley Eastern, 1992.
1. C.F. Gerald, "Applied Numerical Analysis", 2nd Edn., Addison Wesley Publishing Company (For Unit I) 1978, 4th Edn., 1989.