teaching:topics:calculus:notation
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teaching:topics:calculus:notation [2021/05/02 12:13] simon [Why three?] |
teaching:topics:calculus:notation [2024/05/03 18:51] simon [Leibniz] |
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| \begin{align*}%% | \begin{align*}%% | ||
| - | \frac{{\rm d}y}{{\rm d}x} &&& \text{is the ratio of the instantaneous changes in two related values} \\ | + | \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} \\ | + | \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) \\ | + | \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*} | ||
| 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 | ||
teaching/topics/calculus/notation.txt · Last modified: 2024/05/10 11:13 by simon
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