MAT37x
Franklin College
Spring2004
Erich Prisner,
We have one independent variable, usually denoted, t for time, and f(t) is a vector in threedimensional space. Thus f(t)=(f_{1}(t),f_{2}(t),f_{3}(t))we call it the coordinates of a point at time t. We call the equations x=f_{1}(t), y=f_{2}(t), z=f_{3}(t) parametric, where t is the parameter.
Name  Picture  Equations  
Astroid 
 
Cardioid 
 
Double Folium 

The velocity of the point is the derivative of f, i,e, the function f'(t) = (f_{1}'(t),f_{2}'(t),f_{3}'(t)). The speed is the absolute value of the velocity. The acceleration is the second derivative f''(t) = (f_{1}''(t),f_{2}''(t),f_{3}''(t)) of f.
Let T=f'(t)/f'(t) denote the unit tangent vector for time t .