BSc CSIT · Semester III
Numerical Method syllabus
Official TU syllabus for Numerical Method (CSC212): 6 units, 59 topics, 3 credit hours. Every unit links to its notes and solved questions.
1
Solution of Nonlinear Equations
8h · 13 Q- Errors in Numerical Calculations
- Sources of Errors
- Propagation of Errors
- Review of Taylor's Theorem
- Solving Non-linear Equations by 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
Interpolation and Regression
8h · 18 Q- Interpolation vs Extrapolation
- Lagrange's Interpolation
- Newton's Interpolation using divided differences, forward differences and backward differences
- Cubic spline interpolation
- Introduction of Regression
- Regression vs Interpolation
- Least squares method
- Linear Regression
- Non-linear Regression by fitting Exponential and Polynomial
3
Numerical Differentiation and Integration
8h · 11 Q- Differentiating Continuous Functions (Two-Point and Three-Point Formula)
- Differentiating Tabulated Functions by using Newton's Differences
- Maxima and minima of Tabulated Functions
- 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
Solving System of Linear Equations
8h · 12 Q- Review of the existence of solutions and properties of matrices
- Gaussian elimination method
- pivoting
- Gauss-Jordan method
- Inverse of matrix using Gauss-Jordan method
- Matrix factorization and Solving System of Linear Equations by using Dolittle and Cholesky's algorithm
- Iterative Solutions of System of Linear Equations
- Jacobi Iteration Method
- Gauss-Seidal Method
- Eigen values and eigen vectors problems
- Solving eigen value problems using power method
5
Solution of Ordinary Differential Equations
8h · 12 Q- 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
- Solving System of ordinary differential equations
- Solution of the higher order equations
- Boundary value problems
- Shooting method and its algorithm
6
Solution of Partial Differential Equations
5h · 6 Q- Review of partial differential equations
- Classification of partial differential equation
- Deriving difference equations
- Laplacian equation and Poisson's equation
- engineering examples
Textbooks and references
- W. Chency and D. Kincaid, "Numerical Mathematics and Computing", 7th Edition, Brooks/Cole Publishing Co, 2012
- C.F. Gerald and P.O. Wheatley, "Applied Numerical Analysis", 9th Edition, Addison Wesley Publishing Company, New York, 2011
- E. Balagurusamy, "Numerical Methods", Tata McGraw-Hill Publishing Company Ltd., New Delhi, 1999
- W.H. Press, B.P. Flannery et al., "Numerical Recipes: Art of Scientific Computing", 3rd Edition, Cambridge Press, 2007.
- J. M. Mathews and K. Fink, "Numerical Methods using MATLAB", 4rd Edition, Prentice Hall Publication, 2004
Study CSC212 the smart way
Solved questions, flashcards & practice