Syllabus of SYBScITQT

Unit – I

 * Errors
 * Solutions of Algebraic and Transcendental Equations using - Bisection Method, the Method of False Position, NewtonRaphson Method.
 * Interpolation: Interpolation: - Forward Difference, Backward Difference, Newton’s Forward Difference Interpolation, Newton’s Backward Difference Interpolation, Lagrange’s Interpolation.

Unit- II

 * Solution of simultaneous algebraic equations (linear) using iterative methods: Gauss-Jordan Method, Gauss-Seidel Method.
 * Numerical Integration: Trapezoidal Rule, Simpson’s 1/3 rd and 3/8 th rules.
 * Numerical solution of 1st and 2nd order differential equations: - Taylor series, Euler’s Method, Modified Euler’s Method, Runge-Kutta Method for 1st and 2nd Order Differential Equations.

Unit-III

 * Types of Data, Mean, Variance, measures of skewness and kurtosis based on moments,
 * Bivariate data Covariance, Correlation, Karl Pearson’s coefficient properties of correlation coefficient and derivation of the formula for * * Spearman’ s Rank, correlation coefficient,
 * Regression coefficients and derivation of equation for lines of regression. Fitting of curves: Least square method, Fitting the straight line and parabolic curve,

Unit-IV

 * Random variables: Discrete and Continuous random variables,
 * Probability density function, Probability distribution of random variables, Expected value, Variance.
 * Moments Relation between Raw moments and Central moments.
 * Distributions: Discrete distributions: Uniform, Binomial, Poisson,
 * Continuous distributions: uniform distributions, exponential, (derivation of mean and variance only and state other properties and discuss their applications)
 * Normal distribution state all the properties and its applications.

Unit –V

 * Central Limit theorem (statement only) and problems based on this theorem
 * Sampling distributions of i)sample mean ii) difference in the sample means iii) sample proportion,ans iv) difference in the sample proportions.
 * Test of Hypothesis, Level of Significance, Critical Region, One Tailed and Two Tailed Test ,
 * Test of Significance for large Samples,
 * Student’s ‘t’ Distribution and its applications,
 * Interval Estimation of Population Parameters.

Unit-VI

 * Chi-Square Distribution and its applications,
 * Test of the Goodness of Fit and Independence of Attributes, Contingency Table, Yates Correction
 * Linear Programming: Linear optimization problem, Formulation and Graphical solution, Basic solution and Feasible solution,
 * Primal Simplex Method.