MSE101 Mathematics and Computer Programming

Data Analysis

This course is an introductory course in the analysis of experimental data – and particularly the handling of errors and the fitting of physical models to data, including the estimation of the confidence in the parameters obtained.

This course has been written and delivered by Dr Sam Cooper and Prof David Dye together.

In the lectures, we will use the Peer Instruction approach (video explanation), where students review the notes and/or videos prior to the class session, and then we interactively try problems and do demonstrations in the class, using the learning catalytics software to help manage the interaction.

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In the first two lectures of MSE101 in October, we briefly introduce how to handle uncertainty and errors, distinguish accuracy from precision, plot good scientific graphs and analyse the dimensions in an equation. The notes are here (pdf). The videos are online at youtube in bite-size chunks: Dimensional Analysis (6:27), Appropriate Precision (12:41), Precision and Accuracy (4:37) and Plotting Data (6:40). For the second lecture there is an additional video on combining errors (14:38).  You need to review this material before the class! In class, we’ll do some exercises to apply these ideas and discuss them, so if you haven’t reviewed it first, you’ll be all at sea in the lecture session!

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Later in the MSE101 course, we come back to have a longer, eight lecture, discussion about data and curves and fitting equations to data.

In order to do this, we first review logs, graph sketching, root finding and Taylor and Maclaurin series, which will be familiar to some from high school maths. Then we look at how to integrate a particular function of great importance in science, the Gaussian or Normal distribution. This then gets us ready to look at error analysis and the propagation of errors. From there we can look at linear regression, non-linear curve fitting and finally fitting Gaussian distributions as an example of the general case of non-linear least squares minimisation using chi-squared.

The notes are here (pdf). Each Chapter corresponds to the same numbered lecture – with Chapter 0 containing the ‘administriva.’

There is a tutorial sheet – here.  The data file for the last question is here. NB that it will need renaming to a name such as “weld.csv” – and then is can be read by any text editor, or Matlab. Answers.

The material will be examined in the June first year MSE101 exam.

Videos:

Lecture 1. Introduction (1.1), logs (1.2) and curve sketching (1.3).

Lecture 2. Finding roots using the Bisection (2.1) and Newton-Raphson (2.2) methods (Matlab input for Newton-Raphson method – as a MSWord file*).

Lecture 3.  Writing functions as a power series – Maclaurin and Taylor.

Lecture 4. Gaussian / Normal distributions. Integration (4.1) and the erf function (4.2).

Lecture 5. Propagation of Errors (5.1) and an Example (5.2).

Lecture 6. Linear Regression (6.1) and Worked example in Excel (6.2).

Lecture 7. Fitting some diffusion data (7.1). Non-linear least square fitting (7.2)

Lecture 8. Fitting a Gaussian (8). Excel file here.
(For the xy data for the Gaussian, export as csv from the Excel)

*sorry: WordPress won’t allow plain text filetypes.