Examples of contour in the following topics:
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- We can visualize contours of $f$ given by $f(x, y)=d$ for various values of $d$, and the contour of $g$ given by $g (x, y) = c$.
- Suppose we walk along the contour line with $g = c$.
- In general, the contour lines of $f$ and $g$ may be distinct, so following the contour line for $g = c$, one could intersect with or cross the contour lines of $f$.
- When the contour line for $g = c$ meets contour lines of $f$ tangentially we neither increase nor decrease the value of $f$—that is, when the contour lines touch but do not cross.
- The contour lines of $f$ and $g$ touch when the tangent vectors of the contour lines are parallel.
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- A line integral (sometimes called a path integral, contour integral, or curve integral) is an integral where the function to be integrated is evaluated along a curve.