## WSRESTF - Foundation Studies

### General

**Foundation Studies**This Foundation Studies package will provide you with the basic knowledge required to undertake CREST's MSc in Renewable Energy Systems Technology. For many of you, much of the course will comprise of revision. Please read the information below carefully before you begin

### MATHS

**Why is an understanding of engineering maths necessary?**The CREST MSc is not a heavily mathematical programme, but some elements do require mathematical treatment.

*Read more in the 'Maths Introduction' document below..*After completing this topic, you should understand:

- The mathematical concepts that underpin the more technical modules of the MSc.
- Various mathematical equations in the context of the practical aspects of renewable energy technology.

You will not have to use Taylor Series yourselves, but it is a common way in which useful approximations are generated (eg that sinq can be approximated by q for small angles). There are occasions when lecturers will use this to provide a simpler formulation (eg expressions relating to extreme winds in the Wind II module).

These notes are here simply to remind you what complex numbers are since they are used in AC analysis.

Differential equations arise in thermal analysis (as in Solar I) and to describe water waves (as in the Water Power module). You will not be expected to solve differential equations as part of the course but it is important that you understand where the presented solutions come from, and the role of boundary conditions. Laplace Transforms are not explicitly used in the MSc but they do underpin basic control analysis.

This brief note is simply to introduce the concept of state space analysis so that you will recognise the terminology. You will not be expected to apply this approach yourselves.

These notes are simply to assist you in understanding what a spectral density function is. You will not be expected to manipulate such functions, but they are a handy way to represent wind speed variation (as in Wind I and Wind II modules).

Wind turbines are examined as dynamic systems in Wind II and these notes provide the basis of dynamic analysis. You will not however be expected to manipulate matrices as part of the course.

Basic applied probability and statistics are used to describe stochastic processes like wind speed. You will be expected as part of Wind I and Wind II to undertake straightforward probability calculations. The concept of autocorrelation is used in Wind II to describe the time structure of wind fluctuations.

1. Why do I need maths?

2. Taylor series

3. Complex numbers

4. Differential equations and Laplace transform

5. State space analysis

6. Fourier transform and spectral density functions

7. Matrices and Eigen value analysis

8. Statistics and applied probability