daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2024-10-15 17:17:25 -04:00
parent c1629e4f1a
commit 30086f9517
50 changed files with 1307 additions and 86 deletions
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8
quarto/precalc/functions.qmd
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@@ -1289,11 +1289,11 @@ import IntervalArithmetic
```
```{julia}
I1 = IntervalArithmetic.Interval(-Inf, Inf)
I1 = IntervalArithmetic.interval(-Inf, Inf)
```
```{julia}
I2 = IntervalArithmetic.Interval(0, Inf)
I2 = IntervalArithmetic.interval(0, Inf)
```
The main feature of the package is not to construct intervals, but rather to *rigorously* bound with an interval the output of the image of a closed interval under a function. That is, for a function $f$ and *closed* interval $[a,b]$, a bound for the set $\{f(x) \text{ for } x \text{ in } [a,b]\}$. When `[a,b]` is the domain of $f$, then this is a bound for the range of $f$.
@@ -1303,7 +1303,7 @@ For example the function $f(x) = x^2 + 2$ had a domain of all real $x$, the rang
```{julia}
ab = IntervalArithmetic.Interval(-Inf, Inf)
ab = IntervalArithmetic.interval(-Inf, Inf)
u(x) = x^2 + 2
u(ab)
```
@@ -1344,7 +1344,7 @@ Now consider the evaluation
```{julia}
#| hold: true
f(x) = x^x
I = IntervalArithmetic.Interval(0, Inf)
I = IntervalArithmetic.interval(0, Inf)
f(I)
```