Current UK exam textbooks pass over proofs and mathematical discussions in a hurry to show the ‘how to’ of exam questions. Integration by substitution is a little more than just backwards chain-rule and deserves a fuller treatment. Try this, Let, then, Suppose that there exists a function g, of another variable , such that and …
Formula and completing the square – basic stuff for School maths students expressed loud and clear in Carr’s Synopsis of Elementary Results in 1880 – find a proof of 45 by using ideas in 47 and teach yourself to be a mathematical genius.
Mechanics 1, January 2013, write out complete and now available in my exam bucket: http://jped.co.uk/ExamBucket/exambucket.php.
Back in the classroom after Easter for Mechanics 1 consolidation and revision.
Carr’s 626, in his magical book for Edwardian mathematical autodidacts, provides summary of general solutions for trigonometrical equations useful to STEP and A level students.