Get further into power series using the fascinating Bessel's equation.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
Was it possible that this dangerous driving penalty was issued in error?
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?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Which dilutions can you make using only 10ml pipettes?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Match the descriptions of physical processes to these differential equations.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Use vectors and matrices to explore the symmetries of crystals.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Can you work out what this procedure is doing?