Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
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 calulate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Are these estimates of physical quantities accurate?
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?
Was it possible that this dangerous driving penalty was issued in error?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Analyse these beautiful biological images and attempt to rank them in size order.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the relationship between resistance and temperature
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Match the descriptions of physical processes to these differential equations.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Invent scenarios which would give rise to these probability density functions.
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
When you change the units, do the numbers get bigger or smaller?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Which units would you choose best to fit these situations?
How would you go about estimating populations of dolphins?
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?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.