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calculus

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The calculus of the complex

Calculus has long been key to describing the world. Now fractional calculus is providing new ways of describing complex systems.
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The calculus of the complex

Calculus has long been key to describing the world. Now fractional calculus is providing new ways of describing complex systems.

Article
Intriguing integrals

Intriguing integrals: Part I

What's the integral of xk? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it? Chris Sangwin introduces an ingenious method for deriving the integral from first principles.

Article

Intriguing integrals: Part II

Coming to think of it, is the standard formula for the integral of xk really the best one? Chris Sangwin makes an interesting case that it is not.