Match the descriptions of physical processes to these differential equations.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Look at the advanced way of viewing sin and cos through their power series.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in error?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Invent scenarios which would give rise to these probability density functions.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Build up the concept of the Taylor series
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
Explore how matrices can fix vectors and vector directions.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Use vectors and matrices to explore the symmetries of crystals.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you find the volumes of the mathematical vessels?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which pdfs match the curves?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
Use trigonometry to determine whether solar eclipses on earth can be perfect.