Department of Mechanical Engineering, The University of Louisiana at Lafayette, Lafayette, LA, USA. The study of curvature in geometry and its relationship with differential equations is a central ...

A \textbf {curve} is a graph along with the parametric equations that define it. \index {curve!parametrically defined}\index {parametric equations!definition} } This is a formal definition of the word ...

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...