Pre-uni maths revision

So I'm off to do Aerospace Engineering in September and I've been advised to revise my A level maths as much as possible but of course time between now and when my couse starts is a bit limited.

Obviously I'm going to concentrate on the ones I got lowest UMS marks on (core 4 and 3) but I was wondering what topics do you guys particuarly think I should focus on to prepare myself? I didn't take further maths. Would it be worth me buying a further maths textbook and going through that?

Any advice appreciated

Do not waste your time buying an A-level text, or revising from one, you will just cover lots of stuff you do not need, and waste half of your time.

Well, the content of mathematics in the first year varies depending on the uni, so if possible, look into the module catalogue.

But as general advice, get K.A. Stroud Engineering Mathematics, and work through that (I have worked through about 1/3 of it in my holidays so far...), it is the most popular book for 1st year mathematics, and covers most topics for first year courses (except fourier series, etc...).
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What edition the newest one?

Do not waste your time buying an A-level text, or revising from one, you will just cover lots of stuff you do not need, and waste half of your time.

Well, the content of mathematics in the first year varies depending on the uni, so if possible, look into the module catalogue.

But as general advice, get K.A. Stroud Engineering Mathematics, and work through that (I have worked through about 1/3 of it in my holidays so far...), it is the most popular book for 1st year mathematics, and covers most topics for first year courses (except fourier series, etc...).

Subjects...well as I said depends on the uni but the basics generally are:

- Trigonometry (identities, equations, double angles, compound angles etc)
- Hyperbolic functions & equations
- Even, odd, inverse functions of various things.
- Integration (areas under curves, volumes of solids of revolution, mean, RMS, by parts, by algebraic substitution, by partial fractions, etc.)
- Differentiation (up to optimisation, implicit, parametric)
- Complex numbers (from the basics through to de moivres theorem, exponential form)
- Sequences and series (binomial expansions, APs, GPs)
- Determinants to solve simultaneous equations.
- Vectors in 3 dimensional space.
- Limits by inspection.
- Newton Raphson iterative method.

If you know that stuff, then do:

- Fourier series
- L'Hopitals rules
- Maclaurin and Taylor series
- Differential equations
- Multiple integration, other harder integration stuff.
- Differentiation of multi-variable functions

Hope that is of help to you.

Very good advice. I would highly recommend that book, but be warned, it is only useful for 1st year (the latest is the 6th ED).
However, I would say that, suggesting to someone who's just come out of A-level's to read up on Fourier series/multi-variable differentiation is rather unnecessary. Of course if your interested in it, and want to get ahead that is another matter. Fourier series will probably be taught in 2nd year, tops in 2nd semester of your first year.

OP. I suggest you enjoy your summer, there's no reason to have to be doing much work - after all, the next 3/4 years are going to be v.v.tough. If you must do some work, then buy/borrow that book mentioned above and just run through the trigonometry & calculus. It will all be repeated in your mathematics course (which will be the easiest course in 1st year, by far).
The reason I would recommend only going through trig & calc is because in topics such as fluids,thermo and mechanics they will freely use these topics, so it is useful to know what is going on.

edit: the person who I quoted hasn't gone to university either! I would also urge you to relax and take it easy during summer - yes go through some stuff, but only to familiarise yourself with topics which seem a-bit hazy. Don't go overboard and go to university with a whole load of knowledge regarding 2nd order partial differential equations etc etc
In 1st semester you will be taught everything you've learnt in A-level maths + A-level f.maths. It is easy to understand, and will be your simplest subject at university.

edit: the person who I quoted hasn't gone to university either! I would also urge you to relax and take it easy during summer - yes go through some stuff, but only to familiarise yourself with topics which seem a-bit hazy. Don't go overboard and go to university with a whole load of knowledge regarding 2nd order partial differential equations etc etc
In 1st semester you will be taught everything you've learnt in A-level maths + A-level f.maths. It is easy to understand, and will be your simplest subject at university.

This is true.

Well, you see, everybody in A-level maths/physics said to me: "if only I knew some of this before, so I didn't have to cram so much in now".

So, what I did was look at my modules, determine the hardest ones (mathematics and physics), then study towards the first few weeks of the modules.

And another reason is that I have a mathematics test on the 27th of September to see if I go in the higher or lower group, and I want to be in the accelerated class.

I spend maybe 2-8 hours a day during week days on this, which would otherwise be spent unproductively, I think I have a good balance such that I have been "ticking over" during the summer, ready to "rev up" again. I am not being pushed by anyone but myself, and I enjoy the subject so it is not such a hardship.

End of the day, I want a 1st in my degree, and I will go through hell and high water to get it.


About subjects I listed, my 1st year mathematics course includes Fourier series and the rest that I listed, so that is why I listed them.

Fair enough, it's good that you're determined to get a 1st! I think every university has the 'upper' & 'lower' class for mathematics (in engineering), and any prior revision will almost definitely get you in the top set. In fact, most will be madly hungover and won't be able to integrate x^2.

I do agree that otherwise the time would be spent doing unproductive things, and it is going to benefit you for university.

If mathematics is getting abit monotonous, I would suggest picking up a book on one of the other modules and looking at doing some light reading.
For mech/civil/aero students feel free to take out Meriam & Kraige Engineering Statics & Dynamics. One of the basic mechanics book, and very useful. Since you're doing EE Jack, I don't really see them using much of the knowledge in this book

Subjects...well as I said depends on the uni but the basics generally are:

- Trigonometry (identities, equations, double angles, compound angles etc)
- Hyperbolic functions & equations
- Even, odd, inverse functions of various things.
- Integration (areas under curves, volumes of solids of revolution, mean, RMS, by parts, by algebraic substitution, by partial fractions, etc.)
- Differentiation (up to optimisation, implicit, parametric)
- Complex numbers (from the basics through to de moivres theorem, exponential form)
- Sequences and series (binomial expansions, APs, GPs)
- Determinants to solve simultaneous equations.
- Vectors in 3 dimensional space.
- Limits by inspection.
- Newton Raphson iterative method.

If you know that stuff, then do:

- Fourier series
- L'Hopitals rules
- Maclaurin and Taylor series
- Differential equations
- Multiple integration, other harder integration stuff.
- Differentiation of multi-variable functions

Hope that is of help to you.

This is true.

Well, you see, everybody in A-level maths/physics said to me: "if only I knew some of this before, so I didn't have to cram so much in now".

So, what I did was look at my modules, determine the hardest ones (mathematics and physics), then study towards the first few weeks of the modules.

And another reason is that I have a mathematics test on the 27th of September to see if I go in the higher or lower group, and I want to be in the accelerated class.

I spend maybe 2-8 hours a day during week days on this, which would otherwise be spent unproductively, I think I have a good balance such that I have been "ticking over" during the summer, ready to "rev up" again. I am not being pushed by anyone but myself, and I enjoy the subject so it is not such a hardship.

End of the day, I want a 1st in my degree, and I will go through hell and high water to get it.


About subjects I listed, my 1st year mathematics course includes Fourier series and the rest that I listed, so that is why I listed them.