Lectures: The detailed description.
Lab: The methods taught in lecture classes are to be implemented in Matlab. Following is the list of experiments:
Experiment 1: Find a root of non-linear equation f(x) = 0 using bisection and fixed-point iteration methods.
Experiment 2: Find a root of non-linear equation f(x) = 0 using Newton's and secant methods.
Experiment 3: Solve system of linear equations using Gauss elimination method.
Experiment 4: Write LU Factorization of coefficient matrix using Gauss elimination method.
Experiment 5: Solve system of linear equations using Gauss-Seidel and SOR iterative methods.
Experiment 6: Find a dominant eigen-value and associated eigen-vector by Power method.
Experiment 7: Implement Lagrange's interpolating polynomials of degree ≤ n on n+1 discrete data points.
Experiment 8: Implement Newton's divided difference interpolating polynomials for n+1 discrete data points.
Experiment 9: Integrate a function numerically using composite trapezoidal and Simpson’s rule.
Experiment 10: Find the solution of initial value problem using modified Euler and Runge-Kutta (fourth-order) methods.
Text and References:
1. Richard L. Burden, J. Douglas Faires, and Annette M. Burden, Numerical Analysis, CENEGAGE/Brooks Cole, 10th edition, 2015.
2. K. Atkinson and W. Han, Elementary Numerical Analysis, 3rd edition, John Willey & Sons, 2004.
3. Brian Bradie, A Friendly Introduction to Numerical Analysis, Pearson Publishers, 2006.
4. Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, McGraw-Hill Higher Education; 6th edition, 2010.
Course Learning Outcomes (CLO):
Upon completion of this course, the students will be able to:
1. understand the errors, source of error and its effect on any numerical computations and also analysis the efficiency of any numerical algorithms.
2. learn how to obtain numerical solution of nonlinear equations using bisection, secant, Newton, and fixed-point iteration method
3. solve system of linear equations numerically using direct and iterative methods.
4. understand how to approximate the functions using interpolating polynomials.
5. learn how to solve definite integrals and initial value problems numerically.
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