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MA2266 NUMERICAL METHODS UNIT I TESTING OF HYPOTHESIS Sampling distributions - Tests for single mean, Proportion, Difference of means (large and small samples) Tests for single variance and equality of variances chi-square test for goodness of fit Independence of attributes. UNIT II DESIGN OF EXPERIMENTS Completely randomized design Randomized block design Latin square design - 22 factorial design. UNIT III SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS Newton-Raphson method- Gauss Elimination method Pivoting - Gauss-Jordan methods Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method . UNIT IV INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION Lagrange s and Newton s divided difference interpolation Newton s forward and backward difference interpolation - Approximation of derivatives using interpolation polynomials - Numerical integration using Trapezoidal and Simpson s 1/3 rules. UNIT V NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS Taylor s series method - Euler s method - Modified Euler s method - Fourth order Runge-Kutta method for solving first and second order equations - Milne s predictorcorrector methods for solving first order equations - Finite difference methods for solving second order equation. L = 45 T = 15 Total = 60 Periods

 

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