Numerical Methods
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Course Title: Numerical Methods
Course No: BIT203
Nature of the Course: Theory + Lab
Semester: 3
Full Marks: 60 + 20 + 20
Pass Marks: 24 + 8 + 8
Credit Hours: 3
Course Description
Course Objectives
Course Contents
1.1. Errors in Numerical Calculations
- Sources of Errors
- Propagation of Errors
- Review of Taylor's Theorem
1.2. Concept of Non-linear Equations and Solving Methods
- Trial and Error Method
- Bisection Method
- Newton Raphson Method
- Secant Method
- Fixed Point Method
- False Position Method
- Newton's Method for Calculating Multiple Roots
- Evaluating Polynomials with Horner's Method
2.1. Interpolation
- Concept of Interpolation and Extrapolation
- Lagrange's Interpolation
- Newton's Interpolation using divided differences
- Newton's Interpolation using forward differences
- Newton's Interpolation using backward differences
2.2. Regression
- Concept of Regression
- Regression vs. Interpolation
- Least Squares Methods
- Linear Regression
- Non-linear Regression: Exponential and Polynomial
3.1. Numerical Differentiation
- Concept of Differentiation
- Differentiating Continuous Functions (Two-Point and Three Point Formula)
- Differentiating Tabulated Functions by using Newton's Differences
- Maxima and minima of Tabulated Functions
3.2. Numerical Integration
- Concept of Integration
- Newton-Cote's Quadrature Formulas
- Trapezoidal rule
- Multi-Segment Trapezoidal rule
- Simpson's 1/3 rule
- Multi-Segment Simpson's 1/3 rule
- Simpson's 3/8 rule
- Multi-Segment Simpson's 3/8 rule
4.1. Direct Methods
- Existence of Solutions, Properties of Matrices, Matrix Representation
- Gaussian Elimination Method, Partial and Complete Pivoting
- Gauss-Jordan method
- Inverse of matrix using Gauss-Jordan method
4.3. Iterative Solutions of System of Linear Equations
- Jacobi Iteration Method
- Gauss-Seidal Method
5.1. Initial Value Problems
- Concept of Differential Equations
- Initial Value Problem
- Taylor Series Method
- Euler's Method
- Heun's Method
- Runge-Kutta Methods
5.2. Higher Order and Boundary Value Problems
- Solving System of Ordinary Differential Equations
- Solution of the Higher Order Equations
- Boundary Value Problems
- Shooting Method
Laboratory Works
- 1.Non-linear equations
- 2.System of linear equations
- 3.Interpolation and Regression
- 4.Numerical integration and differentiation
- 5.Solving ordinary and partial differential equations
Text Books
- 1.W. Chency and D. Kincaid, "Numerical Mathematics and Computing", 7th Edition, Brooks Cole Publisher
- 2.C.F. Gerald and P.O. Wheatley, "Applied Numerical Analysis", 9th Edition, Addison Wesley Publisher
Reference Books
- 1.W.H. Press, B.P. Flannery et al., "Numerical Recipes: Art of Scientific Computing", 3rd Edition, Cambridge Press.
- 2.J. M. Mathews and K. Fink, "Numerical Methods using MATLAB", 4th Edition, Prentice Hall Publication