ajb

This is called an interpretation - some 'wordy' description of a mathematical framework or calculation. This is a different question. This is backwards. A theory is a mathematical model and then one can build interpretations.

You asking about benchtop gravitational experiments? I know that people do think about such things - but I can not recall who right now!

I have given you a whole area of study - classical mechanics - that is used widely in engineering. You would like me to find a paper that uses classical mechanics? There are lots that use the notions to different degrees - see what you can find. Anyway, classical mechanics is used in the study of robotics, air craft, space craft etc. Basic notions of statics are used in the analysis of stability and equilibrium of structures.

I do not think that this is great English - anyway, just drop 'elite' from future posts. It may not seem so rude when translated to Turkish, but in English it is a rather strange and insulting thing to say. Anyway, we are way off topic here!

In English saying that you are elite is exactly saying that you are better than all or most of the members here.

It is strange and impolite to imply that you are better than someone else. I promise you that by keep saying that you are elite will not gain you any friends.

You should stop calling yourself elite - it is rather self-centred and annoying. Anyway, back on topic... is there anything else about the applications of mathematics in engineering you want to know?

Illogical and unethical seem to mean "I do not agree" lol

But it is! Go to your library and pick up a book with the title something like 'Engineering Mathematics'. It will be full of series and transforms - they should also give some reasonable examples.

Yes, but other series and expansions are used in engineering - a quick look at a few wikipedia pages will tell you more.

I think Hawking is talking about the possibility of higher dimensional space-times, so something like 9+1 dimensional space-time. Everyone in physics and engineering is okay with working with spaces that are of dimension greater than 3, they come up quite naturally in classical mechanics, thermodynamics and so on. But this is not the same as the 3+1 dimensional space-time as given in relativity. And here is a random picture of someone explaining Fourier series...????

I think you mean 4D plus dimensional space-times rather than the use of higher dimensional spaces in physics and engineering in general. I am not sure what you are looking for. You want some sketches involved in some calculations that use Fourier series? Just google that yourself.

Fourier series is used all over the place when a periodic signals/phenomena are present. For example i) Signal and image processing ii) Finding solutions to the heat equation and similar iii) In the theory of small perturbations iv) Acoustics v) Optics etc etc etc Other related things like z-transforms and so on are also used throughout engineering.

I still don't understand - you want me to show you a picture of what?

I don't understand. What are you objecting to?

I am not quite sure what you are asking, but various sequences and expansions are used in engineering all the time. The two common series are of course the Taylor series and the Fourier series.

So classical mechanics does not correlate to reality? (with the standard assumptions of domain of validity and so on.)

Anyway, lots of people in physics and engineering use spaces of dimension greater than 3 (even infinite dimensions).

You seem to want to bring it back to bashing pure maths!

You only cite things that are related no matter what the subject. It is hard to say, but for sure you cannot compare across subjects. There are different habits and traditions across different subjects. The impact factor only takes into account citations of papers that are published in the previous two years - in more theoretical and mathematical subjects it can take longer than two years for a paper to pick up citations. Thus, mathematical journals tend to have low IF as compared to say medical journals. Anyway, this seems to be getting off topic.

Just simple classical mechanics of particles or bodies we need position and then we need some information about how the system evolves. In particular, as we usually have first order differential equations we need to also consider the velocity ; also we are often interested in phase dynamics and so we need momentum.

Well, lots of scientists will not cite such a paper unless they are working on something similar. You have made the great mistake of trying to compare impact factor across different disciplines. You clearly cannot do this, and so your request is just meaningless.

What are you talking about? Many good journals publish works in the areas I have stated here.

Okay, but the basic ideas are not so hard and this is what you are asking about. Anyway, we regularly deal with spaces of dimension greater than three in classical mechanics, statistical physics, thermodynamics and so on. All areas of physics that have found direct applications in engineering and so on.