Syllabus of SYBScITQT
Unit – I
- 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.