Course Syllabi: UMA007 : Numerical Analysis (L : T : P :: 3 : 1 : 2)

 

1.      Course number and name: UMA007 : Numerical Analysis

 

2.      Credits and contact hours: 4.5 and 6

 

3.      Text book, title, author, and year

 

Text Books / Reference Books

         Curtis F. Gerald and  Patrick O. Wheatley,  Applied Numerical Analysis, Pearson, (2003) 7th Edition, 

         M. K. Jain, S .R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publishers (2012), 6th edition.

         Steven C. Chappra, Numerical Methods for Engineers, McGraw-Hill Higher Education; 7th  edition (1 March 2014)

         J. H. Mathew, Numerical Methods for Mathematics, Science and Engineering, Prentice Hall, (1992) 2nd edition, 

         Richard L. Burden and  J. Douglas Faires, Numerical Analysis, Brooks Cole (2004), 8th edition. 

         K. Atkinson and W. Han, Elementary Numerical Analysis,  John Willey & Sons (2004), 3rd Edition.

 

a.       Other supplemental materials

         Nil

 

4.      Specific course information

a.       Brief description of the content of the course (catalog description)

Floating-Point Numbers: Floating-point representation, rounding, chopping, error analysis, conditioning and stability.

Non-Linear Equations: Bisection, secant, fixed-point iteration,  Newton method for simple and multiple roots, their  convergence analysis and order of convergence.

Linear Systems and Eigen-Values: Gauss elimination method using pivoting strategies, LU decomposition, Gauss-Seidel and successive-over-relaxation (SOR) iteration methods and their convergence, ill and well conditioned systems, Rayleigh's power method for eigen-values and eigen-vectors.

Interpolation and Approximations:  Finite differences, Newton's forward and backward  interpolation, Lagrange and Newton's divided difference interpolation formulas with error analysis, least square approximations.

Numerical Integration: Newton-Cotes quadrature formulae (Trapezoidal and Simpson's rules) and their error analysis, Gauss-Legendre quadrature formulae.

Differential Equations: Solution of initial value problems using Picard, Taylor series, Euler's and Runge-Kutta methods (up to fourth-order), system of first-order differential equations.

Laboratory Work: Lab experiments will be set in consonance with materials covered in the theory. Implementation of numerical techniques using MATLAB.

 

5.      Specific goals for the course

After the completion of the course, the students will be able to:

         Understand the errors, source of error and its effect on any numerical computations and also analysis the efficiency of any numerical algorithms.

         Learn how to obtain numerical solution of nonlinear equations using bisection, secant, newton, and fixed-point iteration methods.

         Solve system of linear equations numerically using direct and iterative methods.

         Understand how to approximate the functions using interpolating polynomials. 

         Learn how to solve definite integrals and initial value problems numerically.

 

6.      Brief list of topics to be covered

      Floating-Point Numbers

      Non-Linear Equations

      Linear Systems and Eigen-Values

      Interpolation and Approximations

      Numerical Integration

      Differential Equations