teaching:topics:calculus:notation
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
teaching:topics:calculus:notation [2024/05/03 18:51] simon [Leibniz] |
teaching:topics:calculus:notation [2024/05/10 10:48] simon [Leibniz] |
||
|---|---|---|---|
| Line 79: | Line 79: | ||
| many of the other fields where calculus is used. It is a more mathematical perspective. It was developed | many of the other fields where calculus is used. It is a more mathematical perspective. It was developed | ||
| simultaneously with Newton's notation. | simultaneously with Newton's notation. | ||
| + | \[\frac{{\rm d}y}{{\rm d}x}\] | ||
| + | is the ratio of the instantaneous changes in two related values, | ||
| + | \[\frac{\rm d}{{\rm d}t}(4t^2+3)\] | ||
| + | is between the values of the expression and the variable. | ||
| + | \[\text{repeated:}\quad\frac{{\rm d}^2}{{\rm d}x^2}(3x^3+5) &&& \text{means:}\quad\frac{\rm d}{{\rm d}x}\left(\frac{{\rm d}}{{\rm d}x}(3x^3+5)\right).\] | ||
| + | \[\int_a^b\!x^2 + 4x\,{\rm d}x\] | ||
| + | is the definite integral of the expression taken from `a` to `b`. | ||
| - | \begin{align*}%% | ||
| - | \frac{{\rm d}y}{{\rm d}x} &&& \text{is the ratio of the instantaneous changes in two related values} \\ \\ | ||
| - | \frac{\rm d}{{\rm d}t}(4t^2+3) &&& \text{is between the values of the expression and the variable} \\ \\ | ||
| - | \text{repeated:}\quad\frac{{\rm d}^2}{{\rm d}x^2}(3x^3+5) &&& \text{means:}\quad\frac{\rm d}{{\rm d}x}\left(\frac{{\rm d}}{{\rm d}x}(3x^3+5)\right) \\ \\ | ||
| - | \int_a^b\!x^2 + 4x\,{\rm d}x &&& \text{is the definite integral of the expression taken from }a\text{ to }b | ||
| - | %%\end{align*} | ||
| The kind of calculus that we deal with at school treats each of these as a single symbol, but it does | The kind of calculus that we deal with at school treats each of these as a single symbol, but it does | ||
| make sense to break them down into their parts, considering say \(\ {\rm d}x\ \) on its own. Doing so | make sense to break them down into their parts, considering say \(\ {\rm d}x\ \) on its own. Doing so | ||
teaching/topics/calculus/notation.txt ยท Last modified: 2024/05/10 11:13 by simon
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
