Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How would you go about estimating populations of dolphins?
Was it possible that this dangerous driving penalty was issued in error?
Who will be the first investor to pay off their debt?
Get some practice using big and small numbers in chemistry.
Use vectors and matrices to explore the symmetries of crystals.
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
Can you find the volumes of the mathematical vessels?
Can you make matrices which will fix one lucky vector and crush another to zero?
Match the charts of these functions to the charts of their integrals.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which of these infinitely deep vessels will eventually full up?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Go on a vector walk and determine which points on the walk are closest to the origin.
Why MUST these statistical statements probably be at least a little bit wrong?
Work out the numerical values for these physical quantities.
Explore the relationship between resistance and temperature
How do you choose your planting levels to minimise the total loss at harvest time?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
When you change the units, do the numbers get bigger or smaller?
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?
Are these estimates of physical quantities accurate?
Explore the properties of perspective drawing.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which units would you choose best to fit these situations?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the shape of a square after it is transformed by the action of a matrix.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Can you match these equations to these graphs?
Explore the properties of matrix transformations with these 10 stimulating questions.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you work out what this procedure is doing?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...