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Introduction to Vector

Introduction to Vector Fields

Change of Coordinates

Change of Coordinates and Jacobians

Fubini's Theorem

Fubini's Theorem

Stokes' Theorem

Stokes' Theorem

Divergence Theorem

Divergence Theorem

Triple Integrals in

Triple Integrals in Spherical Coordinates

Spherical Coordinates

Spherical Coordinates

Riemann Sum Definition

Riemann Sum Definition of Double Integrals

Lagrange Multipliers and

Lagrange Multipliers and the Multivariable Extreme Value Theorem

Gradients of Surfaces

Gradients of Surfaces

Lagrange Multipliers

Lagrange Multipliers

Critical Points of

Critical Points of Surfaces

Partial Derivatives of

Partial Derivatives of Surfaces and Tangent Planes

Surfaces and Contour

Surfaces and Contour Plots

Curvature and the

Curvature and the Osculating Circle

Tangential and Normal

Tangential and Normal Components of Acceleration

The Tangent Vector

The Tangent Vector and Normal Vector are Perpendicular!

Arc Length of

Arc Length of Parametric Curves

The Tangent and

The Tangent and Normal Vectors of Curves

Distances between Points,

Distances between Points, Lines, and Planes in 3D (continued)

Distances between Points,

Distances between Points, Lines, and Planes in 3D

Planes in 3D

Planes in 3D

Lines in 3D

Lines in 3D

Geometric Interpretations of

Geometric Interpretations of Dot and Cross Product