MATH36022 Online Resources (2019)
See the course syllabus and see how this course fits in the Numerical Analysis Pathway.
Feedback on the June 2019 exam is available here.
Thank you for filling in Week 3 feedback forms. My response to your comments is here.
You will need to use MATLAB occasionally and should know how to set up vectors, perform mathematical operations on vectors, write simple programmes and plot functions. If you are not confident with MATLAB don't panic. Examples will be given on handouts. Many useful MATLAB resources and tutorials can be found on the web, including, HERE.
Occasionally, we will need results from analysis from earlier courses. These results are summarised in the above document. Students are expected to know these results and should be prepared to use them during the course wherever necessary.
Handouts & Lecture Notes
Online materials (handouts), to read in between lectures, will be provided below. If you prefer paper copies, let me know. A full set of lecture notes will be provided on Blackboard . I recommend reading these only after we've discussed the material in class. Students are expected to take their own notes in the lectures. Anyone with special support needs or special circumstances preventing them from attending lectures should contact me to make arrangements.
Acknowledgement: The notes have been adapted from notes written by Nick Higham for an older version of this course.
Section 1: Approximation of functions
We have now finished this section. Full lecture notes for Section 1 are available on Blackboard.
- Lecture 0: Introduction
- Lecture 1: Polynomials - evaluation and Lagrange interpolation (revision)
- Lecture 2: Chebyshev polynomials
- Lecture 3: Best approximation and norms
- Lecture 4: Interpolation with Chebyshev points
- Lecture 5: Polynomials and linear independence
- Lecture 6: Legendre polynomials
- Lecture 7: Introduction to Pade approximation
- Lecture 8: Evaluating Pade approximations
Section 2: Quadrature
We have now finished this section. Full lecture notes for Section 2 are available on Blackboard.
- Lecture 9: Introduction to quadrature
- Lecture 10: Error in midpoint rule
- Lecture 11: Introduction to Gauss quadrature
- Lecture 12: Gauss rules and weight functions
- Lecture 13: Adaptive quadrature with trapezium rule
Section 3: Numerical methods for solving ODEs
Full lecture notes for Section 3 are available on Blackboard.
- Lecture 15: Example IVPs for ODEs
- Lecture 16: Euler's method
- Lecture 17: Introduction to RK methods (the improved Euler method)
- Lecture 18: m-stage Runge Kutta methods - Read after Week 10 lectures.
- Lecture 20: Euler-Trapezium Predictor-Corrector method - Read after Week 10 lectures.
Of all the text books that appear on the official reading list, the one I recommend most is:
- Endre Suli and David F. Mayers. An Introduction to Numerical Analysis. Cambridge University Press, Cambridge, UK, 2003
The mid-term test has now taken place. This is worth 20% of the overall mark for the course.
Exam resources and feedback
Tutorials will provide an opportunity for students' work to be
discussed and provide feedback on their understanding. Coursework or
in-class tests (where applicable) also provide an opportunity for
students to receive feedback. Students can also get feedback on
their understanding directly from the lecturer, for example during
the lecturer's office hour.
Recent (2018, 2017 and 2016) past exam papers are avaliable from the School of Mathematics website. Note - I did not teach the course in 2018.
Feedback report on the May 2017 exam.
Feedback report on the June 2016 exam.