📐 Unit 9: Parametric, Polar & Vectors

Master curves, coordinates, and motion in multiple dimensions

📊 Parametric Equations

9.1

Parametric Equations: dy/dx

Learn to find derivatives of parametric equations using the chain rule and parameter t

dy/dt dx/dt Chain Rule

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9.2

Parametric Second Derivative

Master finding d²y/dx² for parametric curves and analyze concavity

d²y/dx² Concavity Inflection Points

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9.3

Arc Length of Parametric Curves

Calculate the distance along parametric curves using integration

Arc Length Integration Distance Formula

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🎯 Vector-Valued Functions

9.4

Derivatives of Vector Functions

Differentiate vector-valued functions component-wise for velocity and acceleration

Vector Calculus r'(t) Components

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9.5

Integrating Vector Functions

Find position vectors through integration and solve initial value problems

Integration Antiderivatives Position Vectors

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9.6

Motion in the Plane

Analyze particle motion using parametric and vector-valued functions

Velocity Acceleration Speed Distance

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⭕ Polar Coordinates

9.7

Polar Derivatives

Find slopes of tangent lines to polar curves using dy/dθ and dx/dθ

r(θ) dy/dθ Tangent Lines

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9.8

Area of Polar Regions

Calculate areas enclosed by single polar curves using definite integrals

Area Formula ½r² Integration Polar Regions

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9.9

Area Between Polar Curves

Find areas bounded by two or more polar curves with intersection points

Multiple Curves Intersections Complex Regions

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