Sub : NUMERICAL METHODS
Code : EG 601 SH
Sem : III/I
Theory : 80
Assmnt : 20
Lab : 50
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Total : 150
Syllabus:
1. Solution of Nonlinear Equations
-Review of calculus, continuity, differentiability, intermediate value theorem, Taylor's theorem
-Absolute, relative and round off errors, error bounds for computational errors
-Bisection method, its error bounds and convergence
-Newton's method, secant method anf their convergence
-fixed point iteration, its convergence properties
-zeroes of polynomials by Horner's method
2. Interpolation and Approximation
-Taylor's polynomial approximation, Lagrange's interpolation
- Newton's interpolation and divided difference
-iterative interpolation
-cubic spline interpolation
-leaast squares method of fitting continuous and discrete data or functions
3. Numerical Differentiation and Integration
-Numerical differentiation formulas
-Newtin-Cote's numerical integration formulas, composite numerical integraiton
-Romberg integration algorithm
-Gaussian Integration formulas
4. Linear Algebraic equation
-Review of the properties of matrices
-matrix form of Gauss elimination, pivoting strategies, ill conditioning
-Cholesky's and related algorithms for matrix factorization
Eigen values and eigen vectors and the power method
5. Solution of ordinary Differential Equation
-Euler;s method for solving ordinary differential equations of 1st order and other related methods
- Runge Kutta methods
-Extension to higher order equations
initial value problem
-boundary value problems
6. Solution of partial differential equations
-introduction to the solution of partial differential equations
-engineerig examples
Books:
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- W. Cheney and D. Kincad, "Numerical Mathematic and computing", Edition, Brooks/Cole publishing Co. 1985
- CF Gerald and PO wheatley, "Applied Numerical Analysis", 4th edition, Addison-Wesley publishing Company, New york
-S. Yakowitz and F. Szidarovszky," An Introduction to numerical computations", 2nd Edition, Macmillan publishing Co., New York
Syllabus Typed By:
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Mr. Samir Thapa
http://www.samirthapa.com.np
samirthapa@engineer.com
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