Optimisation
An example of optimisation is finding least cost – in electrical transmission thicker wires reduce power losses but cost more – differentiation tells us the wire thickness leading to least overall cost. Please view the video here.
Partial differentiation
Sometimes two or more independent variables are at play. For example, in a range of hills, our altitude depends on both x- and y- co-ordinates. The concept of partial differentiation is introduced. Please view the video here.
Two way optimisation
Using partial differentiation, we find the best “burn time’’ and elevation angle for a maroon (a rocket that summons assistance). Please view the video here.
Time to have a go
For the homework, we want our ship to “limp home’’ on auxiliary engines – what is the best course and speed, and what masses of fuel and supplies are needed. Please identify diagrams, physical laws and assumptions in this optimisation. You are welcome to try the mathematics – but it is challenging, and we provide the full solution should you struggle. You can find the homework here: homework pdf file.
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