Chapter 10 - Parametric/Polar/Vector Notes

A set of flashcards summarizing key concepts from Chapter 10 on Parametric, Polar, and Vector mathematics.

Parametric Speed

The speed of a particle in parametric form, calculated as v = √((dx/dt)² + (dy/dt)²).

Parametric Arc Length

The length of a curve defined parametrically, calculated as S = ∫√((dx/dt)² + (dy/dt)²) dt.

Parametric Position

The position at time t in parametric equations, given by x(t₂) = x(t₁) + ∫x'(t) dt.

Polar Conversion

The transformation of Cartesian coordinates (x,y) to polar coordinates (r,θ) expressed as x = rcos(θ) and y = rsin(θ).

Polar Area

The area enclosed by a polar curve r(θ), calculated using the formula A = (1/2)∫r² dθ.

Interpretation of Signs in Polar Coordinates

In polar coordinates, if dr and dθ are both the same sign, the point is moving away from the pole; if different signs, it is moving closer.

Period of Polar Shapes

Be cautious that the period of polar shapes may not always be 2π, depending on the specific shape.

Slivers in Integration

When calculating the area or arc length of shapes, be careful about integral changes due to intersecting different shapes.