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Latest Vector Calculus Notes
An Inner Product on the Set of Functions
The Divergence Theorem in Terms of Forms
Stoke's Theorem and 1 - Forms
Derivation of Green's Theorem From Stoke's Theorem in Terms of Forms
Existence of a 1 - Form With Differential Equal to a Given 2 - Form
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Vector Calculus
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Proof That Differentials and Derivatives of Orthogonal Coordinates Form Reciprocal Systems
Proof That Div is a Linear Operator
Proof That Divergence of Curl of a Vector Field is Zero
Proof That Divergence of the Cross Product of a Constant Vector With Radial Vector is Zero
Proof That For an Ellipse, the Dot Product of the Curve With the Cross Product of the Tangent Vector With the Second Derivative is Zero
Proof That Grad f is in the Direction of Greatest Rate of Increase of f
Proof That Harmonic Function Equal on a Closed Surface are Equal on the Enclosed Volume
Proof That If a Harmonic Function Zero on a Surface is Zero Interior to the Surface
Proof That Integral Between Two Points is Independent of Path If the Integral of a Vector Field Around Any Closed Path is Zero
Proof That Integral of Curl of a Vector Field Dot Product Normal is Zero Over a Closed Surface
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