diff --git a/src/2_coordinates.md b/src/2_coordinates.md index a2ca17723440a2484980629850597b331f0bb11a..780b9394573f3d42fa0cfe78721aa251f032a7fa 100644 --- a/src/2_coordinates.md +++ b/src/2_coordinates.md @@ -87,7 +87,7 @@ $$\begin{equation} y = r \sin \varphi.\end{equation}$$ <figcaption></figcaption> </figure> -The inverse relation is given as: +#### The inverse relation !!! info "Inverse relation between polar and Cartesian coordinate systems" \begin{equation} r=\sqrt{x^2 + y^2}; \label{rxy}\end{equation} @@ -195,7 +195,7 @@ of a function of $r, \varphi$ in terms of $x$? For this, we need to realize that there are relations between the coordinate systems. In particular, $r = r(x,y)$ and $\varphi = \varphi(x, y)$ as defined in equations -\ref{rxy} and \ref{phixy}. In fact, we have been rather sloppy in our notation above, +of the [inverse relations](#The-inverse-relation). In fact, we have been rather sloppy in our notation above, as the functions $f(x,y)$ and $f(r, \varphi)$ do not mean that I substitute $x=r$ and $y=\varphi$! It is more precise to state that there are two diferent functions $f_\text{cart}(x,y)$ and $f_\text{polar}(r, \varphi)$ that are equivalent,