Numerical Analysis
Teacher
Satyabrata Sadangi
Category
Core Courses
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Course Name : Numerical Analysis
Code(Credit) : CUTM1518(3-2-1)
Course Objectives
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.
Course Outcomes
| COs | Course outcomes | Mapping Cos with POs (High-3, Medium-2, Low-1) |
| CO1 | · Perform error analysis to select an appropriate numerical model and to estimate errors in numerical solution of a given problem.
|
PO1(3), PO2(2), PO9(3) |
| CO2 | · 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.
|
PO1(3), PO9(3) |
| CO5 | · Analyze and evaluate the accuracy of common numerical methods.
|
PO5(3), PO9(2) |
Course Syllabus
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
Text Book:
- A Course on Numerical Analysis : B. P. Acharya & R. N. Das, Kalyani Publisher
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)
Reference Books:
- K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods For Scientific And Engineering Computation, 6th Ed., New Age International Publisher, India, 2007.
- John H. Mathews and Kurtis D. Fink, Numerical Methods Using MatLab, 4th Ed., Phi Learning Private Limited, 2012.
Session Plan
Session 1
Introduction to Numerical analysis
https://www.youtube.com/watch?v=8qB5HK9j0Y4
https://www.slideshare.net/mohammadtawfik/01-introduction-to-computational-material-engineering
Session 5
Dealing with Errors: relative, absolute, round off, truncation
Session 6 & 7
Practice 1:
Calculate the sum 1+1/2+1/3+1/4+------------+1/N using python
Session 8 & 9
Practice 2:
To find the absolute value of an integer using python
Session 10 & 11
Practice 3:
Enter 100 integers into an array and sort them in an ascending order using python
Session 12
Transcendental and polynomial equations: bisection method
Session 19 & 20
Practice 4:
To find the approximate value of a polynomial using Bisection method.
Session 21 & 22
Practice 5:
To find the approximate value of a polynomial using Newton Rapshon method
Session 23 & 24
Practice 6:
To find the approximate value of a polynomial using Secant method
Session 25 & 26
Practice 7
To find the approximate value of a polynomial using Regula Falsi method
Session 27 & 28
Project 1:
Numerical Methods for Solving Systems of Nonlinear Equations
https://www.lakeheadu.ca/sites/default/files/uploads/77/docs/RemaniFinal.pdf
Session 29 & 30
Project 2:
A Study on Transcendental and Polynomial equations.
https://cims.nyu.edu/~donev/Teaching/NMI-Fall2010/Lecture6.handout.pdf
Session 31
Polynomial Interpolation, Existence and uniqueness of interpolating polynomials
Session 33
Solved Problems on Lagrange’s interpolating polynomial
Session 34 & 35
Practice 8:
To find the value of a function using Lagrange interpolation
Session 36 & 37
Project 3:
A study on Lagrange interpolation
https://ccrma.stanford.edu/~jos/pasp/Lagrange_Interpolation.html
Session 38
Newtons Divided Difference Interpolating Polynomial
Session 39
Forward and backward Difference operators
Session 40
Newtons Forward Difference Interpolating Polynomial
Session 41
Newtons Backward Difference Interpolating Polynomial
Session 42 & 43
Practice 9:
Solving problems on Newton forward/backward difference formula.
Session 44 & 45
Project 4:
A study to apply Newton forward difference formula on solving numerical problems with MATLAB program
https://myclassbook.org/newtons-forward-interpolation-formula-matlab-program/
Session 46 & 47
Project 5:
A study to apply Newton backward difference formula on solving numerical problems.
https://mat.iitm.ac.in/home/sryedida/public_html/caimna/interpolation/nbdf.html
Session 53 & 54
Practice 10:
Solving a problem on trapezoidal rule using python
Session 55 & 56
Practice 11:
Solving a problem on Simpson’s 1/3 rd rule using python
Session 59
Numerical solution of Differential Equation
Session 63 & 64
Practice 12:
Solving Problems on 4th order Runge-Kutta method using python
https://math.okstate.edu/people/yqwang/teaching/math4513_fall11/Notes/rungekutta.pdf
Session 65 & 66
Project 6:
A Study on Runge-Kutta method
https://math.okstate.edu/people/yqwang/teaching/math4513_fall11/Notes/rungekutta.pdf
Case Studies
Case Studies
Our Main Teachers
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 […]