Module information#

All dates below are subject to change.

Module leader : Dr Thomas Ranner (Tom)

Email : T.Ranner@leeds.ac.uk

Teams group : 23/24(1) COMP2421 Numerical Computation (32879)

Course contents#

  • Vectors and matrices: introduction and justification; vector and matrix operations; identity matrix; inverse of a matrix.

  • Approximation and errors: modelling and mathematical modelling; discrete and continuous models; floating point and rounding errors; balancing accuracy and efficiency.

  • Static systems: iterative methods for solving nonlinear scalar equations; methods for solving linear systems of equations; systems without unique solutions.

  • Evolving systems: derivatives and rates of change; initial value problems; stability and convergence of computer models.

Module components#

Lectures#

2 hours per week

  • Thursdays at 12:00

  • Fridays at 11:00

Tutorials#

1 hour per week face to face (see timetable)

Opportunity to get feedback on learning

Worksheets#

These will be provided weekly throughout the semester.

Assessment#

Table 1 Assessment schedule#

Title

Release date

Due date

Credit

Portfolio

Mon 2 Oct

weekly, Tuesday 2pm

20%

Coursework

Mon 4 Dec

Wed 20 Dec, 2pm

80%

Formative 1

Mon 9 Oct

Wed 25 Oct, 2pm

0%

Formative 2

Mon 15 Nov

Wed 29 Nov, 2pm

0%

The dates are tentative at this stage and are subject to change.

Portfolio (20%)#

  • A question similar to each worksheet is available in minerva each week.

  • You will have to submit your answer (and show your working) by the Tuesday 2pm deadline.

  • You will receive two mark for giving the correct numerical and one mark for your working.

  • The best 6 of 8 will count for your final mark.

  • No late submission allowed.

Table 2 Portfolio deadlines#

Section

Deadline

1

Tue 17 Oct, 2pm

2

Tue 24 Oct, 2pm

3

Tue 7 Nov, 2pm

4

Tue 14 Nov, 2pm

5

Tue 21 Nov, 2pm

6

Tue 28 Nov, 2pm

7

Tue 5 Dec, 2pm

8

Tue 12 Dec, 2pm

Summative coursework (80%)#

A single piece of summative coursework will count for the majority of the assessment of this module (80%). You will be asked an open ended question which allows you to explore one of the topics from the module in detail. The rubric that you will be marked against is available in minerva. The coursework will be submitted via Gradescope. Usual late submission rules apply.

Formative coursework#

There will be two additional formative courseworks which you can use to build skills related to the summative coursework. Submission and feedback mechanism details to be confirmed.

Syllabus#

This is a rough breakdown of topics to be covered this semester. Please note that this is not entirely fixed and I cannot guarantee to follow this precise structure.

Table 3 Teaching plan#

Lecture

Topic

1 (week 1)

Introduction

2

Vectors and matrices

3 (week 2)

Floating point numbers

4

Introduction to systems of linear equations

5 (week 3)

Solving triangular systems

6

Gaussian elimination

7 (week 4)

LU factorisation

8

The effects of finite precision

reading week

9 (week 6)

Iterative methods

10

Sparse matrices and stopping criteria

11 (week 7)

Derivatives and rates of change

12

Euler’s method

13 (week 8)

Midpoint method

14

Systems of differential equations

15 (week 9)

Introduction to nonlinear equations

16

Newton’s method

17 (week 10)

Quasi-Newton methods

18

Robust linear solvers

19/20 (week 11)

Special topics/Formative coursework feedback

Tutorials plan#

Weekly tutorials should will support you in your learning. See your timetable for when and where you should attend.

Week

Topic

1

Maths preliminary

2

Introduction to python

3

Floating point number systems

4

Triangular systems and Gaussian elimination

reading week

6

LU Factorisation and iterative methods

7

Sparse systems/pivoting

8

Derivatives and Euler’s method

9

Other time stepping

10

Bisection and Newton’s method

11

Other root finding

Contact#

Reference materials#

The programming for this module will be carried out using python3.