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...technique called SONAR (SOund Navigation And Ranging) revolutionised the investigation of the oceans' depths. Originally developed for hunting submarines, in sonar a ship sends out a pulse of sound (a 'ping'), which is reflected by the target and the reflected sound wave is detected. It was soon realised that if they were 'loud' enough the underwater pings could detect...

...techniques to be hot worked >0.6 Tm. Aluminium alloys can be produced, e.g. Al-4%Cu alloy, as can new compositions and rapidly solidified materials. Alloy steels and stainless steels are preformed on the Osprey Process. Cu-10%Sn bronze preforms with grain sizes of <0.0015 mm can be hot worked without cracking. Heat treatment times for homogenisation are substantially...

...techniques for proving inequalities. Section 4 introduces the concept of a least upper bound. Section 5 looks at how least upper bounds can be used to define arithmetic operations on the set of real numbers...This free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by...