Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which line graph, equations and physical processes go together?
Explore the properties of matrix transformations with these 10 stimulating questions.
Invent scenarios which would give rise to these probability density functions.
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.
Use vectors and matrices to explore the symmetries of crystals.
Why MUST these statistical statements probably be at least a little bit wrong?
How much energy has gone into warming the planet?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How do you choose your planting levels to minimise the total loss at harvest time?
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.
Which of these infinitely deep vessels will eventually full up?
Can you construct a cubic equation with a certain distance between its turning points?
Was it possible that this dangerous driving penalty was issued in error?
Which dilutions can you make using only 10ml pipettes?
Can you find the volumes of the mathematical vessels?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
Get some practice using big and small numbers in chemistry.
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Explore the properties of perspective drawing.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Get further into power series using the fascinating Bessel's equation.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
When you change the units, do the numbers get bigger or smaller?