diff --git a/docs/1b/math119.md b/docs/1b/math119.md index c113a40..1256ce3 100644 --- a/docs/1b/math119.md +++ b/docs/1b/math119.md @@ -2,4 +2,24 @@ ## Multivariable functions +!!! definition + - A **multivariable function** accepts more than one independent variable, e.g., $f(x, y)$. + +The signature of multivariable functions is indicated in the form *[identifier]*: *[input type]* → *[return type]*. Where $n$ is the number of inputs: + +$$f: \mathbb R^n \to \mathbb R$$ + +!!! example + The following function is in the form $f: \mathbb R^2\to\mathbb R$ and maps two variables into one called $z$ via function $f$. + + $$(x,y)\longmapsto z=f(x,y)$$ + ### Sketching multivariable functions + +!!! definition + - In a **scalar field**, each point in space is assigned a number. For example, topography or altitude maps are scalar fields. + - A **level curve** is a slice of a three-dimensional graph by setting to a general variable $f(x, y)=k$. It is effectively a series of contour plots set in a three-dimensional plane. + - A **contour plot** is a graph obtained by substituting a constant for $k$ in a level curve. + +Please see [level set](https://en.wikipedia.org/wiki/Level_set) and [contour line](https://en.wikipedia.org/wiki/Contour_line) for example images.f +