COURSE OBJECTIVES:
● This course aims at providing the necessary basic concepts of a few statistical and numerical
methods and give procedures for solving numerically different kinds of problems occurring in
engineering and technology.
● To acquaint the knowledge of testing of hypothesis for small and large samples which plays
an important role in real life problems.
● To introduce the basic concepts of solving algebraic and transcendental equations.
● To introduce the numerical techniques of interpolation in various intervals and numerical
techniques of differentiation and integration which plays an important role in engineering and
technology disciplines.
● To acquaint the knowledge of various techniques and methods of solving ordinary differential
equations.
UNIT I TESTING OF HYPOTHESIS
Sampling distributions – Tests for single mean, proportion and 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
One way and two way classifications – Completely randomized design – Randomized block design
– Latin square design – 2
2
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 differential equations – Multi step methods:
Milne’s and Adams – Bash forth predictor corrector methods for solving first order differential
equations.
Part – A
Unit – I Sampling, Hypothesis type I and Type II Error
Unit – II Objective design of experiments , ANOVA, Uses of analysis of variance
Unit –III- Fixed point iteration , Pivoting,. Direct and indirect methods, Eigen value of Jacobi method
Unit – IV .Forward or backward , Divided difference, Simpson, trapezoidal formula
Unit – V –Euler problem, Predictor and corrector methods formula
Part – B
- I) small samples ii) Two sample problems (8 + 8)
Unit II 1. Randomize Block Design(RBD) (16 marks )
Unit – III 1. Eigen value and eigen vector of power method (b questions) (8 Marks) - Gauss Elimination methods (8 marks)
Unit – IV 1. Double integral (B questions (8 Marks)
2.Lagranges (8 marks)
Unit – V 1. Taylors method (8 Marks
2.Runge-Kutta Four the order problem (8 |Marks
NOTE : Only focus the above area you may score 80 marks