Unit – I
|Errors, Solutions of Algebraic and Transcendental Equations using – Bisection Method, the Method of False Position, Newton-Raphsonn Method.|
Interpolation: Interpolation: – Forward Difference, Backward Difference, Newton’s Forward Difference Interpolation, Newton’s Backward Difference Interpolation, Lagrange’s
|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.
|Data 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 the 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.
Practical List to be performed in Scilab:
1. Practical 1: Solution of algebraic and transcendental equations:
a. Program to solve algebraic and transcendental equation by bisection method.
b. Program to solve algebraic and transcendental equation by false position method.
c. Program to solve algebraic and transcendental equation by Newton Raphson method.
2. Practical 2: Interpolation
a. Program for Newton’s forward interpolation.
b. Program for Newton’s backward interpolation.
c. Program for Lagrange’s interpolation.
3. Practical 3: Solving linear system of equations by iterative methods:
a. Program for solving linear system of equations using Gauss Jordan methods.
b. Program for solving linear system of equations using Gauss Seidel methods.
4. Practical 4: Numerical Integration
a. Program for numerical integration using Trapezoidal rule.
b. Program for numerical integration using Simpson’s 1/3rd rule.
c. Program for numerical integration using Simpson’s 3/8th rule.
5. Practical 5: Solution of differential equations:
a. Program to solve differential equation using Euler’s method
b. Program to solve differential equation using modified Euler’s method.
c. Program to solve differential equation using Runge-kutta 2nd order and 4th order methods.
6. Practical 6: Random number generation and distributions
a. Program for random number generation using various techniques.
b. Program for fitting of Binomial Distribution.
c. Program for fitting of Poisson Distribution.
d. Program for fitting of Negative Binomial Distribution.
7. Practical 7: Moments, Correlation and Regression
a. Computation of raw and central moments, and measures of skewness and kurtosis.
b. Computation of correlation coefficient and Fitting of lines of Regression ( Raw and
Frequency data )
c. Spearman’s rank correlation coefficient.
8. Practical 8: Fitting of straight lines and second degree curves
a. Curve fitting by Principle of least squares. ( Fitting of a straight line, Second degree curve)
9. Practical 9: Sampling:
a. Model sampling from Binomial and Poisson Populations.
b. Model sampling from Uniform, Normal and Exponential Populations.
c. Large sample tests-( Single mean, difference between means, single proportion, difference between proportions, difference between standard deviations.)
d. Tests based on students ‘t-test’( Single mean, difference between means and paired
10. Practical 10: Chi-square test and LPP
a. Test based on Chi-square- Distribution ( Test for variance, goodness of Fit,)
b. Chi-square test of independence of attributes.
c. Solution of LPP by Simplex method.
Introductory Methods of Numerical Methods, Vol-2, S.S.Shastri, PHI
Fundamentals of Mathematical Statistics, S.C.Gupta, V.K.Kapoor
Elements of Applied Mathematics, Volume 1 and 2, P.N.Wartikar and J.N.Wartikar, A. V.
Engineering Mathematics, Vol-2, S.S.Shastri, PHI
Applied Numerical Methods for Engineers using SCILAB and C, Robert J.Schilling and Sandra L.Harris, Thomson Brooks/Cole
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