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Note: I am not sure if this should be posted here, but, after looking through the other sites, I felt this was the best fit for the question.

For class, I have to make a video with applications of calculus. However, I need a overarching theme to base my applications off of (it has to be something that can be easily followed.) I have no issues whatsoever coming up with applications - that's the easy part (Calculus is very useful!).

In past years, others have made their theme relating to a movie and went that route. No idea really jumped out at me though. So, I figured I would ask you guys if you had any great ideas for a theme.

If you have any suggestions, that would be great. Thank you.

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Calculus is all about change. Derivatives are rates of change. Integrals are sums of changes. You could say something like "We live in a world which is a constantly changing...and Calculus is the language of change." This would allow you to look at applications in more than just Physics but also biology, finance, etc. –  Bill Cook Mar 24 '12 at 0:25
    
Hmm. Not a bad idea, thanks. –  Joe Mar 24 '12 at 0:32

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up vote 5 down vote accepted

How about Engineering? We use Calculus a lot! You can even have "sub-themes" pertaining to the major branches.

Mechanical Engineering for instance uses a large amount of Calculus for Heat Transfer and Fluid Mechanics.

Turbulence in Fluid Flow itself is such an interesting theme. I could make a documentary only on Turbulence.

Aerospace Engineers use differential equations and Calculus of variations for their trajectory design. A lot of other fields come together for designing the spacecraft. The motion of space vehicles is governed by a 6 DOF equation set which is basically a group of ODEs.

Civil Engineering uses Calculus for Structural Analysis.

Electrical and Computer Engineering uses it a lot for analysis of circuits. Signal Processing has its roots in Calculus. Laplace Transforms form the basis for Control Systems.

Industrial Engineers use Calculus for Optimization. This field is huge. Starting from KKT all the way to Global Optimization. Everything is based on Calculus. Be it financial markets, healthcare or production, it can be solved through LP or NLP.

Other fields such as Nuclear, Chemical, Textile etc. also use Calculus for interesting applications. Its not too tough to find out where.

Medicine also uses a lot of Calculus (Actually, its a combination of Biomedical and Industrial Engineering). They use Optimization tools to predict tumours, their malignancy and also for deciding the dosage of radiations (among many other things). Here (PDF) is a good paper on Radiation Optimization.

The list is endless.

Note: These are all examples of Advanced Calculus (ODEs/PDEs/Improper Integrals etc.). If you want applications of Elementary Calculus, you can still look into Engineering to find interesting applications. Either way, the applications can be found which can be intuitive, simple and yet profound.

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Upvoted. Good answer, thanks. –  Joe Mar 24 '12 at 13:42

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