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Browse Classroom Capsules and Notes

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Displaying 1 - 10 of 47

The author presents a geometric interpretation of Leibniz's rule for differentiating under the integral sign, and gives an informal visual derivation of the rule.

The author presents a variety of double and triple integrals designed to exercise a student's ability to visualize the interplay between an integrand and the region over which it is...

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

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

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.

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 classifies the quadratic forms defined by simple 2 by 2 matrices and illustrates them with corresponding quadratic surfaces.

An alternative way to evaluate the famous improper integral of Gauss, \(\int_{0}^{\infty} e^{-x^2} dx\)

The author uses the concept of maximum and minimum values to find Fermat points for a triangle. (The Fermat point of a triangle is the point such that the distances from the vertices have a...