__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; 7 ^{th} 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