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