Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Why MUST these statistical statements probably be at least a little bit wrong?
Which units would you choose best to fit these situations?
Look at the advanced way of viewing sin and cos through their power series.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Formulate and investigate a simple mathematical model for the design of a table mat.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which of these infinitely deep vessels will eventually full up?
Use vectors and matrices to explore the symmetries of crystals.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you find the volumes of the mathematical vessels?
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Which pdfs match the curves?
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?
How would you go about estimating populations of dolphins?
Who will be the first investor to pay off their debt?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Match the descriptions of physical processes to these differential equations.
Match the charts of these functions to the charts of their integrals.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?