Statistics and Numerical Methods

Product: Theory Subject
Categories: Engineering
Department: Common Subjects

Features Includes:

  • 123 - 3D/2D Animation
  • 828 Pages of Content
  • 60 Lecture Hours
  • 284 Solved Problems
  • Suitable for All Technical University Syllabus

Course Description

This learning solution provides a clear exposition of essential tools of Testing of Hypothesis, Design of Experiments, Solution of Equations and Eigenvalue Problems, Interpolation and Approximation, Numerical Differentiation and Integration, Initial Value Problems for Ordinary Differential Equations, Boundary Value Problems in Ordinary and Partial Differential Equations.

OBJECTIVES:

  • To familiarize the student with Testing of Hypothesis
  • To develop an understanding of the standard techniques of Design of Experiments
  • To familiarize the student with Solution of Equations and Eigenvalue Problems
  • To familiarize the student with Interpolation and Approximation
  • To develop an understanding of the standard techniques of Numerical Differentiation and Integration
  • To familiarize the student with Initial Value Problems for Ordinary Differential Equations
  • To familiarize the student with Boundary Value Problems in Ordinary and Partial Differential Equations
UNIT I - TESTING OF HYPOTHESIS

Large sample test - Introduction to Large Sample Test - Test of Significance for single Mean - Example Problems. Test of significance for difference of means - Example Problems - Test of significance for difference of standard deviation - Example Problems. Student's t-distribution - Student's t-distribution - Degrees of Freedom - Properties of t-distribution - Test of Significance for Single Mean - Example Problems - Test of Significance for Difference Between Two Means - Example Problems - Test of significance for Difference between two means (dependent samples) - Example Problems - Test of significance of an observed correlation Co-efficient - Example Problems - t-distribution Table. Chi-square Distribution - Introduction - Properties of Chi-square Distribution - Application of Chi-square Distribution - Chi-square test for Goodness of fit - Conditions for Applying Chi-square test - Example Problems - Chi-square test for Independence of Attributes - Example Problems - Chi-square Distribution Table. F–test for equality of population variances - F–test for equality of population variances - Example Problems - F0.01-distreibution Table - F0.05-distreibution Table.

UNIT II - DESIGN OF EXPERIMENTS

Completely randomized design - Introduction - Design of experiments - Analysis of variance - Completely randomized block design - Example Problems. Randomized block design - Randomized block design - Example Problems. Latin square design - Latin square - Steps in constructing latin square - Factorial design Factorial Experiments Example Problems.

UNIT III - SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of algebraic and transcendental equations - Solution of algebraic and transcendental equations - Important properties of equations. The Iteration method - The Iteration method - Example Problems. Newton-Raphson method - Newton-Raphson method - Convergence of Newton-Raphson method - Quadratic convergence of Newton-Raphson method - Newton-Raphson Extended Formula (or) chebyshev's formula of third order - Example Problems. Gauss Elimination method - Gauss Elimination method - Example Problems. Gauss Jordan method - Example Problems. Guass Jacobi iteration method - iterative method - Example Problems. Guass Seidel method - Guass Seidel method - Example Problems. Inverse of a matrix by Gauss Jordan method - Inverse of a matrix - Example Problems. Eigen values of a matrix by power method - Largest Eigenvalue and the corresponding Eigenvector: By power method - Example Problems.

UNIT IV - INTERPOLATION AND APPROXIMATION

Lagrange’s divided difference interpolations - Lagrange’s Interpolation formula - Newton's divided difference interpolation - Divided differences - Example Problem - Newton's divided difference formula - Example Problems - Spline interpolation - Spline interpolation - Cubic spline interpolation - Example Problems. Interpolation - Interpolation - Errors in polynomial interpolation - Finite differences - Forward difference - Backward differences - Example for Backward difference - Central differences - Example Problem - Introduction to Symbolic relations and seperation of symbols - Introduction to Differences of a polynomial - Example Problems. Newton's formulae for interpolation - Newton's formulae for interpolation - Newton's Forward interpolation formulae - Newton's Backward interpolation formulae - Example Problems.

UNIT V - NUMERICAL DIFFERENTIATION AND INTEGRATION

Numerical differentiation - Derivatives using central difference formula - Numerical integration - Numerical integration - Newton - Cote's Quadrature Formula - Trapezoidal rule - Geometrical interpretation - Example Problems - Simpson's 1/3 rule - Example Problems. Romberg’s method - Romberg’s method - Example Problems. Two point and three point Gaussian quadrature formulae - Gauss quadrature - Example Problems - Gaussian quadrature (3-point formula) - Example Problems. Evaluation of double integrals using Trapezoidal method - Evaluation of double integrals using Trapezoidal method - Example Problems. Evaluation of double integrals using Simpson's method - Simpson's method - Example Problems.

UNIT VI - INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Taylor series method - Taylor series method - Example Problems. Euler's method - Euler's method - Example Problems. Improved Euler method - Improved Euler method - Improved Euler method (Heun's method) - Example Problems. Runge-kutta method of fourth order - Runge-kutta methods - Example Problems. Milne’s Predictor corrector method - Milne’s Predictor corrector method - Example Problems. Predictor-corrector method of Adams-Moulton - Adams - bashforth - moulton method - Corrector formula - Procedure of Adams - Bashforth method - Example Problems.

UNIT VII - BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

Finite difference methods for solving two-point linear boundary value problems - Finite difference method to solve ordinary second order differential equation - Finite difference method - Example Problems. Numerical solution of partial differential equations - Numerical solution of partial differential equations - Difference quotients and difference equations - Classification of partial differential equations of the second order - Example Problems. Finite difference techniques for the solution of two dimensional Laplace’s equation - Elliptic equation - Solution of laplace's equation - Example Problems. Poisson’s equation - Poisson’s equation - Example Problems. One dimensional heat flow equation by explicit methods - One dimensional heat equation - Solution of parabolic equations - Example Problems. One dimensional heat flow equation by implicit (Crank Nicholson) methods - Crank nicholson difference scheme for solving parabolic equation - Example Problems. One dimensional wave equation by explicit method - One dimensional wave equation - Example Problems.