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 [2021/05/02 12:14] simon [Leibniz] |
teaching:topics:calculus:notation [2024/05/10 10:44] 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. | ||
\begin{align*}%% | \begin{align*}%% | ||
- | \frac{{\rm d}y}{{\rm d}x} &&& \text{is the ratio of the instantaneous changes in two related values} \\ | + | \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) \\ \\ |
- | \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 | \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*} | %%\end{align*} |