# 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.