桃色视频

This is a self-guided review of mathematics material that will be useful for the core HetSys training modules, and is designed to be completed at your own pace.

Objectives

By the end of this session you should be able to:

manipulate and carry out operations on vectors manipulate and carry out operations on matrices demonstrate a familiarity with basic linear algebra differentiate and integrate functions solve first-order and higher-order ordinary differential equations solve simple cases of some partial differential equations understand foundational concepts in probability and statistics

The material presented here is not intended to be rigorous, but may rather be considered as a pragmatic quick-start guide to the standard of mathematics expected of students enrolled on this course. The booklet developed by Birmingham and Leeds also provides a useful refresher (whether or not you consider yourself a chemist!). This list is incomplete, so if while studying you feel you need to brush up on other areas of mathematics, follow the Supporting Material link at the end of the list below.

1. Vectors
2. Matrices
3. Linear vector spaces
   1. Definitions and useful properties
   2. Matrix operators and change of basis
4. Differentiation and integration
5. Ordinary differential equations
   6. Second-order variation of parameters
   7. Second-order power series method
6. Partial differential equations
   
   1. Fourier series method
   2. Solving PDEs
7. Probability and statistics. For this section, we have produced a that runs entirely in your browser (no login or installation needed): Probability Foundations workshop. It covers the probability axioms, conditional probability and Bayes' rule, random variables (CDF/PDF), expectation and variance, the standard distributions (Gaussian, uniform, exponential, Bernoulli, binomial), and a numerical demonstration of the central limit theorem, with worked examples and automatically-checked exercises.
8. Supporting material on other topics can be found from the

There is a self-assessment test available to gauge your progress. If you feel sufficiently up-to-date on the maths outlined above, feel free to complete the test now! Otherwise, follow the links to work through each section, and then complete the test. For probability and statistics, work through the interactive alongside attempting the test.

Acknowledgement: Much of this online material is taken from , devised by A. J. Hobson, Coventry University. The linear vector spaces and some of the ODE and PDE notes were written by Tiffany Walsh.