CONICS, PARAMETRIC EQUATIONS, POLAR FUNCTIONS, & VECTORS
Conics
and Calculus
Plane Curves and Parametric Equations
What is a parameter?
Discussion & visualization
of parametric functions
Parametric Equations
Graphing
parametric functions (an applet)
Property of Cycloid
with applet
Visualizing cycloids
Visualizing cycloids
Cycloid
applet
Another place to visualize a cycloid
Working with cycloids
Comparing
linear motion to inverted cycloid motion
Cycloid family
Parametric Equations
and
Calculus
Parametric derivatives applet
Finding
tangent lines
to parametric functions
Parametric Equations and Calculus
Polar Coordinates & Polar Graphs
Finding minimum intervals
Finding
tangent lines
to polar curves
Area and Arc Length in Polar Coordinates
Polar derivatives applet
A
polar area
problem
Another
polar area
problem
An even harder polar area problem: outer area traced,
inner
area traced
Area of polar curve
applet
Vectors in the Plane
Review problems
on vector calculus--Go to
Calculus Book III
and choose any topic
Dot Products
Vector-Valued Functions
Velocity and Acceleration
Tangent Vectors and Normal Vectors
Arc Length and Curvature
Miscellaneous
Trace
out an epicycloid
Trace
out a hypocycloid