If you have accepted an offer of a place on our programme, it is a good idea to prepare for your studies. Our MSc students come from various backgrounds, and at the start of the programme there will be several preparatory non-examined modules aimed to fill-in the gaps.

This, however, might be not enough, since these modules are quite intensive. Therefore, it will be of great advantage for you to make an effort to fill-in the any gaps in your background knowledge. The following reading list aims to help with this. It is far too large to be covered fully. Instead, please identify the topic(s) that you are least familiar with and concentrate on them.

The background knowledge desirable to possess at the start of the programme consists of 3 main parts (in random order, all are equally important):

1. Fluid Dynamics
2. Programming and numerical analysis
3. Mathematics

## Fluid Dynamics

And here is the book:

## Programming and numerical analysis

Learn how to compile and run programs.

A very good basic book is: Fortran90 for Engineers and Scientists by Larry R. Nyhoff and Sandford C. Leestma, published by Prentice Hall. There are two editions (same title), one fatter and more expensive than the other. If this proves difficult to buy, Fortran 90/95 for Scientists and Engineers by Stephen Chapman is also very good. This is published by McGraw Hill.

The desirable background on numerical analysis is at the level of Numerical Analysis, R. L. Burden and J. D. Faires, Brooks/Cole 2001.

Fundamentals of Engineering Numerical Analysis by Parviz Moin, published by Cambridge University Press

## Mathematics

• Ordinary differential equations (ODE). Solution of homogenous and non-homogenous ODEs, particularly n-th order linear ODEs. Linear stability.
• Partial differential equations. Basics.
• Vector calculus: gradient, divergence, curl, Gauss theorem, Stokes theorem etc.
• Functional analysis: Fourier transform, Laplace transform.
• Linear algebra: Definition of matrix-vector multiplication, definition of orthogonal matrices and symmetric matrices, eigenvalues, eigenvectors, the characteristic equation, diagonalization, similarity, determinants, rank, solution of linear equations, change of coordinates/basis. Familiarity with the matrix exponential and Jordan canonical form will be useful, but not necessary.

http://joshua.smcvt.edu/linearalgebra/

http://www.numbertheory.org/book/

Basic algebra, calculus and ordinary and partial differential equations is well covered in reference [1] or any book on "Advanced engineering mathematics" such as [2,3] that also include some basic numerical analysis.

1. Introduction to Applied Mathematics, G. Strang, Wellesley Cambridge, 1986.
2. Advanced Engineering Mathematics 6th Edition, K.A. Stroud and D. J. Booth, Palgrave McMillan, 2007.
3. Advanced Engineering Mathematics 9th Edition, E. Kreyzig, Wiley, 2006.

You know all this? Fantastic! Then have a look at engineering beam theory: torsion, bending etc:

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-20-structural-mechanics-fall-2002/

Seems too much? Do what you can and we will try to teach you the rest.

Good luck and see you all in September.

Professor Sergei Chernyshenko - Director of Studies

## AERO97026 Introduction to Fluid Dynamics

As part of the programme, we run a number of compulsory, non-assessed introductory modules that are intended to help ensure that you all have a standard level of knowledge that the rest of the programme will build on.

One of these modules, Introduction to Fluid Dynamics, takes the form of an independent study module. This means that we provide the module materials in an online format for you to follow yourself at home: Fluid Dynamics 2020-21. This will be supported by a few hours of online lectures in August. The online lectures will include lectures on key topics of the course, and revision lectures where you will have an opportunity to ask questions and go over any issues that came up in your study. You are required to follow the course material, which should take you no more than about 20 hours. This must be done before the MSc officially starts on Monday 30th September.

Attending the online lectures is not compulsory, but is strongly encouraged. The exact dates of these online lectures will be decided later.

## AERO97028 Introductory Mathematics

We are also making the  module available to you to complete before teaching commences.