# Browse Classroom Capsules and Notes

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Displaying 91 - 100 of 1209

The author shows that the system characterized by

$$x(t) = a_1 t^2 + b_1 t + c_1$$
$$y(t) = a_2 t^2 + b_2 t + c_2$$
$$z(t) = a_3 t^2 + b_3 t + c_3$$

must lie in a...

Projectile motion on large and small scales in the context of problems from sports

Hands-on activities using balloons for a differential equations class

The Method of Undetermined Coefficients is approached by using linear operators and making use of patterns associated with matrix multiplication.  The authors discuss several pedagogical...

Relations between Romeo and Juliet presented as pairs of coupled differential equations

The author presents a visual proof of the closed form of a recursively defined sequence: $$a_2 = 3$$ and $$a_n = 2 a_{n-1} + 1$$

This article describes and encryption algorithm that can be used to transmit information between two parties such that each person can verify the other person's information.

This article uses a generalization of a three-way gunfight to motivate the construction and solution to a first order linear system of difference equations.  The method of undetermined...

The author presents a visual proof of the formula for the sum of the first n consecutive products: $$1 \times 2 + 2 \times 3 + 3 \times 4 +\ldots + n \times (n+1)$$.

How can we define multiplication of ordered pairs of real numbers to make $$\Re^2$$ into a ring, or field? In this article, the author derives conditions for certain types of rings and extends...