Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Get some practice using big and small numbers in chemistry.
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of matrix transformations with these 10 stimulating questions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How much energy has gone into warming the planet?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Analyse these beautiful biological images and attempt to rank them in size order.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
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?
Which dilutions can you make using only 10ml pipettes?
Explore the shape of a square after it is transformed by the action of a matrix.
Invent scenarios which would give rise to these probability density functions.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out what this procedure is doing?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
Use vectors and matrices to explore the symmetries of crystals.