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Much of physics can be derived from the principle of least action. A more complete answer could fill up several books, so I will just stop here.

http://en.wikipedia.org/wiki/Principle_of_least_action
The most widely used principle: Using an axe.

One of the most important strategy for conquering and solving problems: Divide and Conquer. Divide the problem into individual units and solve the units individually. Finally, piece them up to obtain a complete picture.

One of your resources in doing this is basic differentiation-which divides the problem into parts and integration-summing or piecing up.

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