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To understand the limitations of analytical methods and the need for numerical methods and the ability to apply these numerical methods to obtain the approximate solutions to engineering and mathematical problems. Ability to decide and to derive appropriate numerical methods for approximating the solutions of various types of problems in engineering and science and analyze the error incumbent in any such numerical approximation. Ability to report analysis, solution and results in a standard engineering format.
Perform error analysis to select an appropriate numerical model and to estimate errors in numerical solution of a given problem. Derive a variety of numerical algorithms/methods & compare the viability of different approaches to the numerical solutions of various mathematical problems arising in roots of linear and non-linear equations, interpolation and approximation, numerical differentiation and integration, system of linear algebraic equations and differential equations. Analyze and evaluate the accuracy of common numerical methods.
Module – I (5hr+6hr+0hr)
Introduction to Numerical Analysis, Concept of Number system: Binary numbers, octal numbers, hexa-decimal numbers. Floating point Arithmetic, K – digit Arithmetic, Dealing with Errors: Relative,absolute,roundoff,truncation.
Practice 1: Calculate the sum 1+1/2+1/3+1/4+------------+1/N. using python
Practice 2: To find the absolute value of an integer using python
Practice 3: Enter 100 integers into an array and sort them in an ascending order using python
Module – II (7hr+8hr+4hr)
Numerical Solution of non-linear equations: method of bisection, Regula-falsi method, Secant method, Newton-Rapshon method, fixed point iteration method.
Practice 4: To find the approximate value of a polynomial using Bisection method.
Practice 5: To find the approximate value of a polynomial using Newton Rapshon method
Practice 6: To find the approximate value of a polynomial using Secant method
Practice 7: To find the approximate value of a polynomial using Regula Falsi method
Project 1: Numerical Methods for Solving Systems of Nonlinear Equations
Project 2: A Study on Transcendental and Polynomial equations.
Module – III (3hr+2hr+2hr)
Polynomial Interpolation, Existence and uniqueness of interpolating polynomials, Lagrange’s interpolating polynomial.
Practice 8: To find the value of a function using Lagrange interpolation
Project 3: A study on Lagrange interpolation
Module – IV (4hr+2hr+4hr)
Newtons Divided Difference Interpolating Polynomial, Forward and backward Difference operators. Newton’s Forward and backward Difference Interpolation formula
Practice 9: Solving problems on Newton forward/backward difference formula using python
Project 4: A study on Newton’s Divided Difference Interpolation Formula
Project 5: A study to apply Newton forward difference/backward formula on solving numerical problems with MATLAB program
Module – V ( 5hr+4hr+0hr)
Numerical Integration, Newton-cotes rule, Trapezoidal Rule, Simpsons 1/3 rd rule, Simpsons 3/8 th
Practice 10: Solving a problem on trapezoidal rule using python
Practice 11: Solving a problem on Simpson’s 1/3 rd rule using python
Module – VI (2hr+0hr+0hr)
Compound Quadrature rules, Gauss-Legendre Rules,
Module – VII (4hr+2hr+2hr)
Numerical solution of Differential Equation, Euler’s method, Runge-Kutta 4th order method
Practice 12: Solving Problems on 4th order Runge-Kutta method using python
Project 6: A Study on Runge-Kutta method
Chapters: 1, 2 (2.1 – 2.3, 2.6 - 2.9), 3 (3.1 to 3.4, 3.6 to 3.8). 6 (6.1- 6.3, 6.5, 6.10, 6.11), 7 (7.1, 7.3,7.7)
A study to apply Newton forward difference formula on solving numerical problems with MATLAB program
Mr. Satyabrata Sadangi has received his M.Sc. (Mathematics) from National Institute of Technology(NIT) Rourkela, Orissa, India and B.Ed. from PRSU University, C.G, India. Mr. Sadangi has more than ten years of teaching experience in different educational institutes. Presently he is working as an Assistant Professor, Department of Mathematics, School of Applied Sciences, Centurion University of […]