Study Guides / Case Studies

Essential Mathematics and Statistics for Science, 2nd Edition Graham Currell and Antony Dowman, Wiley-Blackwell, 2009

The 'study guides' provide a sequence of on-line questions, with full video answers, to take you through the main individual calculation steps. The self-assessment questions allow you to find where you may need some tutorial help, and the video answers may act as a sufficient 'tutorial' in themselves. If further help is required, the guides provide links to tutorial material from a range of other sources.

An increasing number of 'case studies' each start with a scientific problem which typically requires several steps to unravel, e.g. analysing typical experimental data or a complex problem involving more than one type of calculation skill. The overall analysis or calculation is demonstrated through video, or linked to sections in the book "Essential Mathematics and Statistics for Science, 2ed".

A typical 'case study' includes hyperlinks to one or more of the 'study guides' that may be required to solve the particular problem.

Study Guides (questions + video answers):

Use of SI Units
- conversion of units, handling 'power' units, using units to check equations
Use of Excel for analysing experimental error/uncertainty
- use of functions and data analysis tools for replicate data and regression calculations
Moles, grams and concentrations
- calculations involving moles, mass, volume, concentrations and dilutions.
Rearranging equations
- rearrangement of equations and formulae
Straight lines and inear regression
- use of the 'best-fit' straight line for interpreting experimental data
Logarithms and exponentials
- mathematics and applications of ex, 10x, and their associated logarithms in science

Case Studies:

Gas Laws pV=nRT (+Video analysis)
- analysis of linear equations - rearrangement, substitution of values, units, straight line analysis, uncertainty - based on the gas law equation.
Arrhenius equation (+Video analysis)
- calculation of the activation energy of a reaction from experimental values of the rate constant of a chemical reaction as a function of temperature.
Beer's Law (+Video analysis)
- use of linear calibration line of absorbance against concentration, including assessment of linearity and uncertainty, including use of Excel 2007 for drawing graphs.
Preparation of Concentration Standards for AAS  (Draft version)
- follows the decisions and calculations required to produce a set of practical concentration standard solutions and calculates instrumental uncertainties.

Experiment / research design (References to the textbook "Essential Mathematics and Statistics for Science", 2nd Ed)
For students who are faced with the problem of designing a new experiment or research project. This study guide identifies the wide range of issues that must be considered in the experiment design process, with links to sections in the book, together with links to relevant electronic resources.
Analysis of exponential growth/decay (References to the textbook "Essential Mathematics and Statistics for Science", 2nd Ed)
This study guide calculates standard times for growth or decay, starting from data values given as a function of time, and assuming an exponential relationship.

Uncertainty and Errors (example calculations)
Propagation of uncertainty - resistivity (Excel 2003)
Propagation of uncertainty - heat capacity (Excel 2003)
Calibration uncertainty – extrapolation errors (Excel 2003)
Calibration uncertainty – method of standard additions (Excel 2003)