Looking at small values of functions. Motivating the existence of the Taylor expansion.
This problem explores the biology behind Rudolph's glowing red nose.
Are these estimates of physical quantities accurate?
Build up the concept of the Taylor series
How would you go about estimating populations of dolphins?
Which units would you choose best to fit these situations?
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.
When you change the units, do the numbers get bigger or smaller?
Work out the numerical values for these physical quantities.
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
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Explore how matrices can fix vectors and vector directions.
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?
Get further into power series using the fascinating Bessel's equation.
Can you match the charts of these functions to the charts of their integrals?
How much energy has gone into warming the planet?
Can you find the volumes of the mathematical vessels?
Explore the properties of matrix transformations with these 10 stimulating questions.
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
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.
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Match the descriptions of physical processes to these differential equations.
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out which processes are represented by the graphs?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Go on a vector walk and determine which points on the walk are closest to the origin.