Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
How would you go about estimating populations of dolphins?
Which line graph, equations and physical processes go together?
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.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Which pdfs match the curves?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Invent scenarios which would give rise to these probability density functions.
Explore the shape of a square after it is transformed by the action of a matrix.
Who will be the first investor to pay off their debt?
Explore the properties of matrix transformations with these 10 stimulating questions.
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Use vectors and matrices to explore the symmetries of crystals.
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which of these infinitely deep vessels will eventually full up?
Explore the meaning of the scalar and vector cross products and see how the two are related.
How do you choose your planting levels to minimise the total loss at harvest time?
Can you find the volumes of the mathematical vessels?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Go on a vector walk and determine which points on the walk are closest to the origin.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Can you make matrices which will fix one lucky vector and crush another to zero?
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 the properties of perspective drawing.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Can you match these equations to these graphs?