Policies

Purpose/Expectations: Under graduate courses in numerical analysis are extremely necessary. Numerical analysis naturally finds applications in all the fields of engineering and physical sciences. The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems. Students are expected to attend every lecture, tutorial, and lab. In order for you to fully benefit from the course, you should start doing homework and assignments. The entire syllabus will be covered approximately in 39 lectures as per schedule given below.

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. 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.

Lab: Students conceptual learning can be significantly enhanced by providing opportunities for students to see and feel the effects of their theoretical analysis.The students are required to implement following programming exercises by using MATLAB programming language. The students are also required to maintain a file of algorithms and input-output of their lab assignments.

Experiment 1: Find the root of non-linear equation f(x) = 0 using bisection and fixed-point iterative methods.

Experiment 2: Find the root of non-linear equation f(x) = 0 using Newton's and secant iterative methods.

Experiment 3: Solve system of linear equations using Gauss elimination method.

Experiment 4: Write LU factorization using Gauss elimination and hence solve the system using LU factorization.

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.