Area Differential (Cartesian Coordinates) Formula |
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| \( dA = dx \cdot dy \) | ||
| Symbol | English | Metric |
| \( dA \) = Area Differential | \( ft^2 \) | \( m^2 \) |
| \( dx \) = Infinitesimally Small Change in x-plane | \( in \) | \( mm \) |
| \( dy \) = Infinitesimally Small Change in y-plane | \( in \) | \( mm \) |
Area differential, abbreviated as \(A\), is an infinitesimally small element of area, represented in calculus as dA. It is used when analyzing surfaces by breaking them into extremely small patches whose dimensions can be treated as constant within each patch. Depending on the coordinate system, the area differential may take different forms. By summing or integrating all these tiny area elements, one can calculate total surface areas, surface integrals, flux, or distributed quantities such as pressure or charge over a surface. The area differential provides a precise mathematical tool for handling surfaces in continuous systems.
Area Differential (Polar Coordinates) Formula |
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| \( dA = r \cdot dr \cdot d\theta \) | ||
| Symbol | English | Metric |
| \( dA \) = Area Differential | \( ft^2 \) | \( m^2 \) |
| \( r \) = Radius | \( ft \) | \( m \) |
| \( dr \) = Infinitesimally Small Change in Radius | \( in \) | \( mm \) |
| \( dy \) = Infinitesimally Small Change in Degree | \( deg \) | \( rad \) |