Browse Classroom Capsules and Notes

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Displaying 41 - 47 of 47

The author revisits formulas of measuring solid angles that he could find only in centuries-old literature, and provides modern versions of the proofs.

The author verifies that a scalar field associated to a vector field, satisfying spherical symmetry and Laplace's equation, implies Newton's inverse square law.

Use Green's Theorem to find a particular integral of a single variable

The author explores the relationship between saddle points of surfaces and the inflection points of the projected curves.

The author shows how to solve a class of analytic functions using an approach demonstrating a surprising connection between multivariable calculus and linear algebra.

The authors prove a necessary and sufficient condition for the existence of the limits of a class of multivariable rational functions commonly seen in textbooks.

The author provides a characterization of $n$-dimensional quadratic functions in terms of tangent planes.