partial differential equation

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Maths in a minute: Differential equations

Change is the only constant in our lives — which is why differential equations are so useful.

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The best of both worlds

Straddling the boundary between pure and applied mathematics.

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Abel Prize 2015: all wrapped up

This year's Abel prize shows you can wrap anything, no matter how weirdly shaped.

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Kelvin's bubble burst again
A new foam with medical potential
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Restoring profanity
In 1979 decorating work in a house in Vienna revealed a set of medieval frescoes depicting a cycle of songs by a 13th century poet, who was particularly fond of satirising the erotic relationships between knights and peasant maidens. The frescoes are of great historical significance, but they are badly damaged. In this article Carola Schönlieb explores how mathematicians use the heat equation to fill in the gaps.
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Career interview: Systems engineer
Chuck Gill caught the space bug as a child when watching Alan Shepherd launch into space. Since then he's worked as a US Air Force navigator, a satellite operator, and in the US intelligence service. These days he's busy reducing carbon emissions and preparing London for the 2012 Olympics. Plus went to see him to find out more about his career.
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Universal pictures
Peter Markowich is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell. Plus went to see him to find out more, and ended up with a pictorial introduction to partial differential equations.
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Career interview: Financial Engineer
Rupa Patel never wanted to be a financial engineer — she wanted to be a maths teacher. However, her skills in conveying difficult mathematical concepts to others, as well as a love of maths, enticed her into the exciting field of financial mathematics. Now she models risk, travels Europe and occasionally finds time to herself to examine the maths of her job in detail.
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Career interview: Project finance consultant
Nick Crawley had recently set up his own financial consultancy firm in Sydney, Australia, offering advice on large-scale financing deals. He tells Plus about the challenges and rewards of working in an incentive-driven environment.
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Career interview: Fluid mechanics researcher
André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.
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How the leopard got its spots
How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Lewis Dartnell solves these, and other, puzzles of animal patterning.
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Going with the flow
Fluid mechanics is the study of flows in both liquids and gases, and is therefore enormously important in understanding many natural phenomena, as well as in industrial applications. Geophysicist Herbert Huppert tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.
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