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.

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.

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,

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.

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.

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.