Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get further into power series using the fascinating Bessel's equation.
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
Invent scenarios which would give rise to these probability density functions.
Can you make matrices which will fix one lucky vector and crush another to zero?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?
Can you find the volumes of the mathematical vessels?
Explore the relationship between resistance and temperature
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which dilutions can you make using only 10ml pipettes?
Which of these infinitely deep vessels will eventually full up?
Match the charts of these functions to the charts of their integrals.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work out the numerical values for these physical quantities.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How do you choose your planting levels to minimise the total loss at harvest time?
Go on a vector walk and determine which points on the walk are closest to the origin.
Are these estimates of physical quantities accurate?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Look at the advanced way of viewing sin and cos through their power series.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the shape of a square after it is transformed by the action of a matrix.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
How would you go about estimating populations of dolphins?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the properties of perspective drawing.
This problem explores the biology behind Rudolph's glowing red nose.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?