MAS212 Scientific Computing and Simulation (2018/19)

Lecturer: Dr Sam Dolan (G18)

The Barnsley Fern

This is the course web page for MAS212 Scientific Computing and Simulation in 2018/19.

This is a previous version of the course - click here for the current academic year.

Course Information

MAS212 is a 10-credit, Level 2, first-semester module which covers various techniques in scientific computing, and their implementation in Python. The course is intended to follow on from MAS115 Mathematical Investigation Skills.


This year I will also use MOLE for some course materials, such as video clips.

Software and setup

We will be using the Anaconda distribution of Python (version 3.6), which includes Jupyter Notebook and Spyder.

Anaconda3 is available on (the majority of) Managed Desktop machines. From the Start Menu, select the folder "Anaconda3 (64-bit)".

To install Anaconda on your own computer, use the link below, and choose the Python 3.6 version

Learning Resources

There are many books on Python and scientific computing. For this course, I recommend:

Copies are available in the library.

A range of material is available on the web, including:

Sample Notebooks

In this course we will use Jupyter notebooks to combine code, text, plots and media. To view a notebook in the browser, click on the links in the left column. (Alternatively, copy-and-paste the notebook's URL in to the box at

To interact and modify a notebook, right-click on a link in the right column (.ipynb) and download to your Jupyter notebook directory.

Fern The Barnsley Fern: an image of a fern with self-similar (fractal) properties, generated by iterating certain affine transformations. .ipynb
ODE_Example Shows how to (a) solve a first-order single-variable ODE using scipy.integrate.odeint, and plot; (b) solve a second-order equation by writing as a pair of first-order equations; (c) solve predator-prey equations. .ipynb
Curve_Fit_Example Shows how to (a) generate a data set with simulated noise; (b) save and then re-load the data; (c) fit the data to a simple model using scipy.optimize.curve_fit(). .ipynb
Media_Example Shows how to load and interact with various media: data, images, web pages, YouTube videos and maps. .ipynb

Lectures and Lab Classes

Week Lectures Computer labs Solutions
0 Revise Python for the class test with: ---
1 L1: Introducing the course Lab Class 1: Jupyter Notebook .html .ipynb
2 L2: Arrays in numpy

The Mandelbrot set:
Class Test 1 (.ipynb) Class Test 1 answers (.html)
3 L3: Plotting Lab Class 3: matplotlib .html .ipynb
4 L4: Ordinary differential equations Lab Class 4: Solving ODEs with scipy.integrate.odeint() .html .ipynb
5 L5: Numerical methods for ODEs Lab Class 5: Explicit methods for ODEs .html .ipynb
6 L6: Implicit methods for ODEs Lab Class 6: Implicit methods for ODEs .html .ipynb
7 Lecture 7: Animations Lab Class 7: Animations
Codes 5 and 6 by J Vanderplas
.html .ipynb
8 Lecture 8: Curve fitting.
Lab Class 8: Fitting data .html .ipynb
9 Lecture 9: Linear systems and conditioning.
Lab Class 9: Gauss-Jordan elimination .html .ipynb
10 Lecture 10: The discrete Fourier transform. Class Test 2 (.ipynb)


# Title Summary Due Feedback
1 Rational approximations Use Python to find rational approximations to real numbers such as sqrt(2), pi and the golden ratio. Sun 21st Oct (23:59pm).
2 Predator-prey equations An investigation into the behaviour of rabbit and fox populations. Sun 25th Nov (23:59pm). Example report

Code: .ipynb .html
3 Pulsars In which you will fit a model function to a data set, to examine the profile of the radio-wave emission from a rotating neutron star. Sun 16th Dec (23:59pm). Example presentation

Class Tests

To take a test, right click on ".ipynb" link, save the file in your notebooks directory (choose 'All Files' not 'Text Documents'), and then open the notebook using Jupyter Notebook. Read the rubric. Then click on a question and select 'Insert Cell Below'. Change the cell type to 'code' or 'markup', as appropriate. Completed tests will be submitted here.

To view a test, left click on the ".html" link.

(2018) Class Test 2 answers .ipynb .html --
(2018) Class Test 1 answers .ipynb .html --
Past tests:
(2017) Class Test 1 with answers .ipynb .html
(2017) Class Test 1 .ipynb .html
(2016) Class Test 1 with answers .ipynb
Marker's notes
(2016) Class Test 1 .ipynb