EP30.FSF1106 — Advanced Numerical Analysis

This course provides an advanced and rigorous study of computational methods used to approximate solutions to mathematical problems in science and engineering. The course develops the theoretical foundations and practical implementations of:

• Direct and iterative methods for solving large linear systems
• Approximation and orthogonal polynomial methods
• Eigenvalue algorithms
• Nonlinear system solvers
• Numerical methods for ODE boundary-value problems
• Numerical methods for elliptic, parabolic, and hyperbolic PDEs

Students will build strong analytical skills (error, stability, convergence analysis) and computational skills (MATLAB/Python implementation). Through weekly labs and a final project, students learn reproducible scientific computing and numerical experimentation.

Requirements for taking final /terminal exams

Students are allowed to take the final exam/terminal exams (50%) if their attendance score (10%) reaches 5 points or more (on the scale of 10).

Requirements for attending classes

Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proofs must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.

Students will be awarded points for constructive comments these points are added to attendance points and group assignments.

Groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.

Requirements for in-class behaviour

The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.

Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.

Laptops and tablets are only used for the purpose of taking notes and calculating for lectures and exercises, absolutely forbidden to use for other purposes.

The course content  is organized into seven chapters: 

• Chapter 1: Direct Methods for Solving Linear Systems
• Chapter 2: Iterative Techniques in Matrix Algebra
• Chapter 3. Approximation Theory
• Chapter 4. Approximating Eigenvalues
• Chapter 5. Numerical Solutions of Nonlinear Systems of Equations
• Chapter 6. Boundary-Value Problems for Ordinary Differential Equations
• Chapter 7. Numerical Solutions to Partial Differential Equations