Differential equations

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Modelling assumptions in mechanics

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
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Bird-brained

Age

16 to 18

Challenge level

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
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Taking trigonometry series-ly

Age

16 to 18

Challenge level

Look at the advanced way of viewing sin and cos through their power series.
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Reaction rates

Age

16 to 18

Challenge level

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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Bessel's equation

Age

16 to 18

Challenge level

Get further into power series using the fascinating Bessel's equation.
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Predator - prey systems

Age

16 to 18

Challenge level

See how differential equations might be used to make a realistic model of a system containing predators and their prey.
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A different differential equation

Age

16 to 18

Challenge level

Explore the properties of this different sort of differential equation.
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What's my equation?

Age

16 to 18

Challenge level

Can you find the differential equations giving rise to these famous solutions?
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It's only a minus sign

Age

16 to 18

Challenge level

Solve these differential equations to see how a minus sign can change the answer
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Differential equation matcher

Age

16 to 18

Challenge level

Match the descriptions of physical processes to these differential equations.