The course aims to provide students with the specialist knowledge in advanced Numerical Analysis. With this overall aim, the course strives to enable students to: Understand analytical, developmental and technical principles that relate to Numerical Linear Algebra, Numerical Methods for solving Differential Equations, and Numerical Optimization, develop the academic abilities required to solve problems and applications in Numerical Analysis and/or Numerical Optimization and critically assess relevant aspects of the industry, and demonstrate an ability to initiate and sustain in - depth research in Numerical Analysis or Numerical methods.

INTENDED LEARNING OUTCOMES

1. Demonstrate understanding of common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems.
2. Apply numerical methods to obtain approximate solutions to mathematical problems.
3. Derive numerical methods for various mathematical operations and tasks, such as interpolation, differentiation, integration, the solution of linear and nonlinear equations, and the solution of differential equations.
4. Analyse and evaluate the accuracy of common and advanced numerical methods.
5. Implement numerical methods in Maple or Matlab.
6. Write efficient, well-documented Maple/Matlab code and present numerical results in an informative way.

Prerequisites: Numerical Analysis

CONTENTS

1. Jacobi method, Gauss seidel method (Application and implementation),
2. SOR (Successive over Relaxation Method),
3. Accelerating Convergence (Linear, quadratic),
4. Aitken's Delta Square Method.
5. Steffensen's Method, Nested Arithmetic, Polynomial Evaluation,
6. Horner's Method of root approximation,
7. Complex root approximation, Muller's Method,
8. Van Wijngaarden-Dekker-Brent Method (Invention, procedure),
9. Laguerre's Method, Golden-section Search Algorithm,
10. Jenkins--Traub Algorithm,
11. Implementation of Numerical methods using Programming Languages.

BOOKS RECOMMENDED

1. Richard L. Burden, J. Douglas Faires, Numerical Analysis, 9th Edition, Brooks /Cole, 2010.
2. Kiusalaas, Jaan. Numerical methods in engineering with Python 3. Cambridge University Press, 2013.

BOOKS SUGGESTED

1. S. C. Chapra and R. P. Canale: Numerical Methods for Engineers, (6th edition, McGraw Hill.2010)
2. Monagan,. Geddes,. Labahn, Maple 7 Programming Guide, Waterloo Maple Inc 2001.

RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS

Research project/assignment based on numerical techniques and algorithms often involve features which require their solutions can be awarded to students during their course work period. Examples of features are

1. Accelerating convergence of numerical methods.
2. Finding numerical solution of analytical complex problems
3. Improving efficiency of numerical techniques

Assessment Criteria

• Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)
• Mid-Term Exam: 30
• Final-Term Exam: 50

Key Dates and Time of Class Meeting

Wednesday/Thurseday                                                           02:00 - 03:30 pm

Commencement of Classes                                                   November 02, 2020

Mid Term Examination                                                            January 11--14, 2021

Final Term Examination                                                          March 01, 2021

Declaration of Result                                                              March 12, 2021