Numerical Method
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Course Title: Numerical Method
Course No: CSC212
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 and Taylor's Theorem
- Errors in Numerical Calculations
- Sources of Errors
- Propagation of Errors
- Review of Taylor's Theorem
1.2. Methods for Solving Non-linear Equations
- Trial and Error method
- Half-Interval method and Convergence
- Newton's method and Convergence
- Secant method and Convergence
- Fixed point iteration and its convergence
- Newton's method for calculating multiple roots
- Horner's method
2.1. Interpolation Methods
- Interpolation vs Extrapolation
- Lagrange's Interpolation
- Newton's Interpolation using divided differences
- Forward differences and backward differences
- Cubic spline interpolation
2.2. Regression Analysis
- Introduction of Regression
- Regression vs Interpolation
- Least squares method
- Linear Regression
- Non-linear Regression by fitting Exponential and Polynomial
3.1. Numerical 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
- 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
- Gaussian integration algorithm
- Romberg integration
4.1. Direct Methods
- Review of the existence of solutions and properties of matrices
- Gaussian elimination method
- Pivoting
- Gauss-Jordan method
- Inverse of matrix using Gauss-Jordan method
4.2. Matrix Factorization
- Matrix factorization
- Solving System of Linear Equations by using Dolittle and Cholesky's algorithm
4.3. Iterative Methods
- Iterative Solutions of System of Linear Equations
- Jacobi Iteration Method
- Gauss-Seidal Method
4.4. Eigenvalue Problems
- Eigen values and eigen vectors problems
- Solving eigen value problems using power method
5.1. Initial Value Problems
- Review of differential equations
- Initial value problem
- Taylor series method
- Picard's method
- Euler's method and its accuracy
- Heun's method
- Runge-Kutta methods
5.2. Advanced ODE Problems
- Solving System of ordinary differential equations
- Solution of the higher order equations
- Boundary value problems
- Shooting method and its algorithm
6.1. Partial Differential Equations
- Review of partial differential equations
- Classification of partial differential equation
- Deriving difference equations
- Laplacian equation and Poisson's equation
- Engineering examples
Laboratory Works
- 1.Program development and testing of non-linear equations
- 2.System of linear equations
- 3.Interpolation
- 4.Numerical integration and differentiation
- 5.Linear algebraic equations
- 6.Ordinary differential equations
- 7.Partial differential equations
Text Books
- 1.W. Chency and D. Kincaid, Numerical Mathematics and Computing, 7th Edition, Brooks/Cole Publishing Co, 2012
- 2.C.F. Gerald and P.O. Wheatley, Applied Numerical Analysis, 9th Edition, Addison Wesley Publishing Company, New York, 2011
Reference Books
- 1.E. Balagurusamy, Numerical Methods, Tata McGraw-Hill Publishing Company Ltd., New Delhi, 1999
- 2.W.H. Press, B.P. Flannery et al., Numerical Recipes: Art of Scientific Computing, 3rd Edition, Cambridge Press, 2007
- 3.J. M. Mathews and K. Fink, Numerical Methods using MATLAB, 4th Edition, Prentice Hall Publication, 2004