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.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Was it possible that this dangerous driving penalty was issued in error?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
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
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Can you match these equations to these graphs?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you work out which processes are represented by the graphs?
Which units would you choose best to fit these situations?
Can you find the volumes of the mathematical vessels?
How much energy has gone into warming the planet?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the properties of matrix transformations with these 10 stimulating questions.
Here are several equations from real life. Can you work out which measurements are possible from each 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?
This problem explores the biology behind Rudolph's glowing red nose.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Invent scenarios which would give rise to these probability density functions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Use vectors and matrices to explore the symmetries of crystals.
Analyse these beautiful biological images and attempt to rank them in size order.
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Are these estimates of physical quantities accurate?
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
Can you make matrices which will fix one lucky vector and crush another to zero?
Who will be the first investor to pay off their debt?
Can you match the charts of these functions to the charts of their integrals?
Explore how matrices can fix vectors and vector directions.