Dot product
38:40Determinants; cross product
52:51Matrices; inverse matrices
51:04Square systems; equations of planes
49:02Parametric equations for lines and curves
50:50Velocity, acceleration; Kepler's second law
48:04Review
49:50Level Curves; Partial Derivatives; Tangent Plane Approximation
46:13Max-Min Problems; Least Squares
49:44Second Derivative Test; Boundaries & Infinity
52:18Differentials; Chain Rule
50:09Gradient; Directional Derivative; Tangent Plane
50:10Lagrange Multipliers
50:10Non-Independent Variables
49:11Partial Differential Equations; Review
45:23Double Integrals
48:00Double Integrals in Polar Coords; Applications
51:30Change of Variables
49:55Vector Fields and Line Integrals in the Plane
51:09Path Independence and Conservative Fields
50:23Gradient Fields and Potential Functions
50:11Green's Theorem
46:45Velocity, acceleration; Kepler's second law
This lecture introduces vector descriptions of velocity and acceleration in three dimensions, culminating in a rigorous derivation and geometric interpretation of Kepler's Second Law of Planetary Motion using calculus.
Lecture 06: Velocity, acceleration; Kepler's second law.
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