gibson:teaching:spring-2016:math445:lecture:loglinear
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gibson:teaching:spring-2016:math445:lecture:loglinear [2016/02/03 13:45] gibson created |
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| ====== Math 445 lecture 4: log-linear relations ====== | ====== Math 445 lecture 4: log-linear relations ====== | ||
| + | ===== Log-linear relations ===== | ||
| Logarithmic plots are useful when the data you're plotting varies over many orders of magnitude. Logarithmic plots can also highlight certain functional relationships | Logarithmic plots are useful when the data you're plotting varies over many orders of magnitude. Logarithmic plots can also highlight certain functional relationships | ||
| ^ plot command ^ functional relationship ^ | ^ plot command ^ functional relationship ^ | ||
| - | | **plot(x,y)** ^ $y = mx + b$ ^ | + | | ''plot(x,y)'' ^ $y = mx + b$ ^ |
| - | | **semilogy(x,y)** | $y = c \; 10^{mx}$ ^ | + | | ''semilogy(x,y)'' | $y = c \; 10^{mx}$ ^ |
| - | | **semilogx(x,y)** | $y = m \log x + b$ ^ | + | | ''semilogx(x,y)'' | $y = m \log x + b$ ^ |
| - | | **loglog(x,y)** | $y = c x^m$ ^ | + | | ''loglog(x,y)'' | $y = c x^m$ ^ |
| - | In lecture I will show (1) why each of these functional relationships appears as a straight line in the corresponding plot command and (2) how to estimate the values of the constants from a graph, in order to estimate $y(x)$ as an explicit function. | + | In lecture I will show (1) why each of these functional relationships appears as a straight line in the corresponding plot command and (2) how to estimate the values of the constants from a graph, in order to estimate $y(x)$ as an explicit function, given a few data points. |
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| + | You can derive these formulae from the log-linear relations instead of memorizing them. For example, you can derive $y = c \; 10^{mx}$ by exponentiating both sides of $\log y = m x + b$. | ||
gibson/teaching/spring-2016/math445/lecture/loglinear.1454535928.txt.gz · Last modified: 2016/02/03 13:45 by gibson
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