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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which pdfs match the curves?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Use vectors and matrices to explore the symmetries of crystals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Invent scenarios which would give rise to these probability density functions.
Which line graph, equations and physical processes go together?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Build up the concept of the Taylor series
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Why MUST these statistical statements probably be at least a little bit wrong?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Analyse these beautiful biological images and attempt to rank them in size order.
Which dilutions can you make using only 10ml pipettes?
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Explore the meaning of the scalar and vector cross products and see how the two are related.
How would you go about estimating populations of dolphins?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which units would you choose best to fit these situations?
Who will be the first investor to pay off their debt?
Match the descriptions of physical processes to these differential equations.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Are these estimates of physical quantities accurate?
Work out the numerical values for these physical quantities.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
When you change the units, do the numbers get bigger or smaller?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Go on a vector walk and determine which points on the walk are closest to the origin.
Is it really greener to go on the bus, or to buy local?
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?
Explore how matrices can fix vectors and vector directions.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How do you choose your planting levels to minimise the total loss at harvest time?