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# Math project- Integration in applied mathematics watch

1. Hello,

I have to write a 3000 words essay (something similar to EPQ/EE but has to be more advanced) in maths.
The highest grades received are in applied mathematics and I decided that I am going to do my research in this field ( I have the greatest interest in it)
A bunch of people told me to look into population dynamics but I must admit that I am not that interested in it and have done my essays in this field
I want my essay to deal something with integration, derivatives and trigonometry. The highest grates receive essays that have applied something in real life and or/ created their own formula.

Personally, I had something in my mind but I cannot shape up the ideas. The angular velocity of a body in an elliptical orbit or something in engineering idk

2. (Original post by BioOx)
Hello,

I have to write a 3000 words essay (something similar to EPQ/EE but has to be more advanced) in maths.
The highest grades received are in applied mathematics and I decided that I am going to do my research in this field ( I have the greatest interest in it)
A bunch of people told me to look into population dynamics but I must admit that I am not that interested in it and have done my essays in this field
I want my essay to deal something with integration, derivatives and trigonometry. The highest grates receive essays that have applied something in real life and or/ created their own formula.

Personally, I had something in my mind but I cannot shape up the ideas. The angular velocity of a body in an elliptical orbit or something in engineering idk

In the real world, the uses of integration are generally (a) for calculating all sorts of things in physics and (b) for finding the areas and volumes of surfaces in engineering (for example). In most cases, the functions that have to be integrated are too complicated to be done algebraically, so computer packages such as Mathematica are used to find a numerical value to any desired degree of accuracy - they generally do this by applying some variant of the Trapezium Rule or Simpson's Rule (which you may have learnt about in your mathematics studies) with many thousands of strips.
So if any of that interests you, perhaps you could derive some of the known formulae for numerical integration and/or create a new algorithm of your own.
The other use of integration that you might think of is in solving differential equations, but most of the DEs that govern important phenomena like atmospheric changes and fluid dispersion actually don't have analytical (algebraic) solutions, so again numerical methods have to be used. This is why weather forecasting companies, for example, use banks of supercomputers that work day and night to calculate what the expected changes in the atmosphere will be based on measurements of the current conditions.
3. (Original post by HapaxOromenon3)
In the real world, the uses of integration are generally (a) for calculating all sorts of things in physics and (b) for finding the areas and volumes of surfaces in engineering (for example). In most cases, the functions that have to be integrated are too complicated to be done algebraically, so computer packages such as Mathematica are used to find a numerical value to any desired degree of accuracy - they generally do this by applying some variant of the Trapezium Rule or Simpson's Rule (which you may have learnt about in your mathematics studies) with many thousands of strips.
So if any of that interests you, perhaps you could derive some of the known formulae for numerical integration and/or create a new algorithm of your own.
The other use of integration that you might think of is in solving differential equations, but most of the DEs that govern important phenomena like atmospheric changes and fluid dispersion actually don't have analytical (algebraic) solutions, so again numerical methods have to be used. This is why weather forecasting companies, for example, use banks of supercomputers that work day and night to calculate what the expected changes in the atmosphere will be based on measurements of the current conditions.
Thank you very much! Could you give me a more specific example?
4. (Original post by BioOx)
Thank you very much! Could you give me a more specific example?
What exactly are you requesting an example of?
5. (Original post by HapaxOromenon3)
What exactly are you requesting an example of?
b) I should not be using anything in regards of software
Engineering
6. (Original post by BioOx)
b) I should not be using anything in regards of software
Engineering
http://www.ijee.ie/articles/Vol18-1/Ijee1262.pdf

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