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Browse Classroom Capsules and Notes

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It is shown that Euler-Cauchy equations with certain types of nonhomogeneous terms can be solved by the method of undetermined coefficients.
The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.
The author finds a more effective way to deal with partial fractions with an irreducible quadratic denominator.

The authors provide a geometric proof for the limit , \(\frac{\sin t}{t}\), simpler than the geometric proof found in most calculus textbooks.

Find the probability of winning a game.
The author presents a visual proof of the well-known formula for the sum of the first n cubes.
It is shown that (b - a)/(ln b - ln a) fits between the arithmetic and geometric mean.

A new technique is described for providing a geometric interpretation of a function of a complex variable.

Two proofs, one from calculus I, one from calculus II, that 1 - x^r < r*(1 - x).