AP Calculus BC

Advanced Placement Calculus BC including series, parametric equations, and polar functions.

Sequences and Series IntroductionConvergence TestsPower Series and Taylor Series
Parametric Equations and CalculusPolar Coordinates and CalculusConvergence and Error in Taylor Series
Modeling Motion with Parametric EquationsSignal Processing with SeriesEngineering with Polar Functions
Mastering Series QuestionsVisualizing Parametric and Polar CurvesBreaking Down Multi-Step Problems
Sequences and Series...Convergence TestsPower Series and Tay...Parametric Equations...Polar Coordinates an...Convergence and Erro...Modeling Motion with...Signal Processing wi...Engineering with Pol...Mastering Series Que...Visualizing Parametr...Breaking Down Multi-...
Practical Applications

Modeling Motion with Parametric Equations

Tracking Motion in the Real World

Parametric equations make it easy to describe and predict paths of moving objects—like basketballs, airplanes, or planets!

How It Works

  • Each object's position can be described as functions of time.
  • Velocity and acceleration can be calculated using derivatives.

Real-World Impact

  • Sports analysts predict ball trajectories.
  • Engineers design roller coaster tracks.
  • Animators create smooth character motions.

Examples

  • A firework follows a parametric path to draw a heart in the sky.

  • A robot arm's tip moves along a parametric curve for precision painting.

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Signal Processing with Series