Numerical methods are now at the heart of applied mathematics. Many significant practical problems cannot be solved by analytical methods - their solutions can only be approximated through numerical methods. Since numerical methods do not give exact solutions to problems it is important to analyse their accuracy. It is also important to understand the stability, efficiency and robustness of a numerical scheme.
This course introduces concepts in numerical analysis emphasising the development of numerical algorithms to provide solutions to common problems formulated in science and engineering. This will develop the basic understanding of numerical algorithms, their computer implementation, applicability and limitations.
- Semester 1 - 2020
On successful completion of the course students will be able to:
1. Understand floating point numbers, computer arithmetic and the role of errors in numerical analysis.
2. Understand the applicability and limitations of a range of important numerical schemes and their role in science and mathematics.
3. Develop their own numerical algorithms for real-world problems, implement them in a computer, visualise and interpret their solutions.
4. Understand accuracy, consistency, stability and convergence of a numerical method, and the concepts of well- and ill-conditioned problems.
- Computer arithmetic
- Solving nonlinear equations
- Numerical differentiation and integration
- Solving systems of linear equations
- Least squares approximation
Written Assignment: Written Assignment 1
Written Assignment: Written Assignment 2
Quiz: In-class quiz
Formal Examination: Final examination
Face to Face On Campus 3 hour(s) per Week for Full Term
Tutorial and computer lab work will be integrated with lectures as required.