18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

1. Vectors and Matrices

Part C: Parametric Equations for Curves

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Parametric equations define trajectories in space or in the plane. Very often we can think of the trajectory as that of a particle moving through space and the parameter as time. In this case, the parametric curve is written (x(t); y(t); z(t)), which gives the position of the particle at time t.

A moving particle also has a velocity and acceleration. These are vectors which vary in time. We will learn to compute them as derivatives of the position vector.

» Session 15: Equations of Lines
» Session 16: Intersection of a Line and a Plane
» Session 17: General Parametric Equations; the Cycloid
» Session 18: Point (Cusp) on Cycloid
» Session 19: Velocity and Acceleration
» Session 20: Velocity and Arc Length
» Session 21: Kepler’s Second Law
» Problem Set 3

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Problem Sets with Solutions
Lecture Videos
Lecture Notes