Look at the advanced way of viewing sin and cos through their power series.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get further into power series using the fascinating Bessel's equation.
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Which units would you choose best to fit these situations?
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?
Was it possible that this dangerous driving penalty was issued in error?
Formulate and investigate a simple mathematical model for the design of a table mat.
Use vectors and matrices to explore the symmetries of crystals.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which pdfs match the curves?
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Match the descriptions of physical processes to these differential equations.
Explore how matrices can fix vectors and vector directions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Can you work out what this procedure is doing?
Analyse these beautiful biological images and attempt to rank them in size order.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Are these estimates of physical quantities accurate?
Can you construct a cubic equation with a certain distance between its turning points?
Can you find the volumes of the mathematical vessels?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?