c14mudd - 18.03 Muddy Card responses 1 The commonest...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
18.03 Muddy Card responses, March 10, 2006 1. The commonest question concerned the idea and utility of operators. I’ll say something now. You can look ahead at the “exponential shift law” if you want, to see one use later. An operator modiFes a function in some way. D differentiates, so Dx = x ˙. [The independent variable isn’t indicated in the notation,, and has to be gleaned from the context. In fact in one of the lectures I muddied the waters further by writing Dx 2 = 2 x , so in that instance the independent variable must have been x . If it had been t , the correct formula would have been Dx 2 = 2 xx ˙, which could aslo be written Dx 2 = 2 xDx .] You can multiply operators and add them. Multiplication means “compose”: so D 2 means “do D twice,” or take the second derivative. If we want to express, say, ¨ x + bx ˙ + kx as the effect of an operator on the function x , we’ll need a symbol for the operator which leaves x alone, the identity operator. Some books use
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online