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

 

8

Lectures

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.

 

8

Lectures

Unit-III 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  equation  for lines of regression.

 

Fitting of curves: Least square  method, Fitting the straight line and  parabolic  curve,

 

8

Lectures

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.

 

8

Lectures

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.

 

 

8

Lectures

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.

 

 

8

Lectures

 

 

Books:

  1. Introductory Methods of Numerical Methods, Vol-2, S.S.Shastri, PHI
  2. Fundamentals of Mathematical Statistics, S.C.Gupta, V.K.Kapoor

 

 

 

Reference:

  1. Elements of Applied Mathematics,  Volume 1 and 2, P.N.Wartikar and J.N.Wartikar, A. V. Griha, Pune
  2. Engineering Mathematics, Vol-2, S.S.Shastri, PHI
  3. Applied  Numerical  Methods  for  Engineers  using  SCILAB  and  C,  Robert  J.Schilling  and
  4. Sandra L.Harris, ” , Thomson Brooks/Cole

 

Term Work: Should contain at least 6 assignments (one per unit) covering the syllabus.

 

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 ‘t’)

 

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.