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From Joseph Biello
Bubbles. Stoke's theorem. -
From Joseph Biello
Stokes' theorem, the divergence theorem. Comparison of the theorems and the fundamental theorem of calculus. -
From Joseph Biello
Parameterization of a spherical surface. The east and south unit vectors. Surface area and surface integrals. -
From Joseph Biello
Parameterized surfaces in three dimensions. The area element of a surface. The normal vector to a surface. -
From Joseph Biello
Green's theorem in its two forms. Examples. -
From Joseph Biello
The definition of the gradient, the divergence, and the curl. -
From Joseph Biello
The directional derivative. Conservative vector fields, conservation of energy. Path independence. -
From Joseph Biello
Circulation and Flux, examples. -
From Joseph Biello
Definition of flow, circulation, and flux of a vector field through (or along) a curve. -
From Joseph Biello
Newton's law of motion and the definition of work. -
From Joseph Biello
Vector fields. Examples of the basic linear vector fields. -
From Joseph Biello
Curvature and the unit normal. Interpretation. Line integrals and averaging. -
From Joseph Biello
Arc length parameterization of curves. The helix. -
From Joseph Biello
Curves in space. Solution of a particle acting under a constant gravitational force and gravity. -
From Joseph Biello
Curve parameterizations and tangent vectors