COURSE INFORMATION

Course Code: MM301

Course Name: Statistics and Numerical Techniques

Contacts: 3L+1T

Credits: 4

COURSE OUTCOME

At the end of this course, the incumbent will be able to:

  1. Remembering: Recalling the basic mathematical tools such as, derivative, real integration, solution of equations, existence of solution of system of linear equations and differential equation.
  2. Understanding: Describe the concept of error, operators and interpolation. Numerical approach of solving missing term, finding of polynomials, integrated value, solution of algebraic equations, system of linear equations and differential equation.
  3. Applying: Use interpolation, integration for data analysis and finding of volume of rough surface. Apply different numerical techniques to solve algebraic equations, system of linear equations in iterative way. Solve boundary value wave and heat equations using differential equations.
  4. Analyzing: Analyze different real time problems and categorize them during the process of solving, by numerical technique mentioned.
  5. Evaluating: Justify and make gradation of above mentioned numerical tools and determine the right approach to find the optimal solution for multidisciplinary engineering problems.
  6. Creating: Design a working model and build a path by which a new approach can be generated to create a new problem appreciated by academics, research & emerging direction in industry.

 

 

PREREQUISITES

To understand this course, the incumbentmust have idea of:

         Derivative of a function and fundamental theorems on calculus

         Taylor series expansion of a single variable function

         Rolleís theorem and Intermediate Value theorem

 

 

SYLLABI

Basic Statistics-measure of central tendency, dispersion, Probability, distribution introduction to mass function, density function, distribution function (Binomial, Poisson,

Normal), estimation of parameters ( unbiasedness-concept of noise/error, consistency)

Interpolation-Newtons Forward, Backward, Sterling & Besselís Interpolation formula,

Lagrange's Interpolation

Integration- Trapezoidal, Simpsonís 1/3 rd, Weddelís Rule, Romberg Integration, Gauss-

Legendre two & three point formula, Newton Cotes Formula.

Gram-Schmidt orthogonalisation, Tchebycheff polynomial

Solution of transcendental equations- Method of Iteration, Method of Bisection, Newton -

Raphson Method, Regula-Falsi method, Secant Method.

Solution of system of linear equations-  Gauss Elimination Method, Gauss-Jacobi, Gauss-Seidel, LU factorisation, Tri-diagonalisation.

Inverse Interpolation.

Least Square Curve fitting- linear & non-linear

Solution of Differential Equations- Picardís method, Euler-modified method, Taylorís

Series method, Runge-Kutta method, Milneís Predictor-Corrector method.

                                                                                                                                         

BEYOND SYLLABI COVERAGE

Gauss Jordan method.

Gauss Jacobi iterative method.

 

LECTURE PLAN

MM301

LECTURE NOTE   

Lecture Notes

 

 

HOMEWORK/ASSIGNMENT

Assignment I

 Assignment II

 Assignment III

 Assignment IV

 Assignment V

Assignment VI(Beyond Syllabus)

 

RECOMMENDED READINGS

TEXT

 

1.      Dutta& Jana: Introductory Numerical Analysis.

2.      Numerical Analysis,  S.N. Mollah

REFERENCE

 

1.      Balagurusamy:      Numerical  Methods, Scitech.