MA8452 – NOTES & QP
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MA8452 – SYLLABUS
UNIT I TESTING OF HYPOTHESIS
Sampling distributions — Estimation of parameters — Statistical hypothesis — Large sample tests based on Normal distribution for single mean and difference of means -Tests based on t, Chi-square and F distributions for mean, variance and proportion — Contingency table (test for independent) — Goodness of fit.
UNIT II DESIGN OF EXPERIMENTS
One way and two way classifications — Completely randomized design — Randomized block design — Latin square design — 22 factorial design.
UNIT III SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of algebraic and transcendental equations — Fixed point iteration method — Newton Raphson method — Solution of linear system of equations — Gauss elimination method — Pivoting — Gauss Jordan method — Iterative methods of Gauss Jacobi and Gauss Seidel — Eigenvalues of a matrix by Power method and Jacobi?s method for symmetric matrices.
UNIT IV INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION
Lagrange?s and Newton?s divided difference interpolations — Newton?s forward and backward difference interpolation — Approximation of derivates using interpolation polynomials — Numerical single and double integrations using Trapezoidal and Simpson?s 1/3 rules.
UNIT V NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Single step methods : Taylor?s series method — Euler?s method — Modified Euler?s method — Fourth order Runge-Kutta method for solving first order equations — Multi step methods : Milne?s and Adams — Bash forth predictor corrector methods for solving first order equations