# Classroom Capsules and Notes

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used in Course Communities. So far we have organized capsules for the following courses:

• One-Variable Calculus
• Sequences and Series
• Multivariable Calculus
• Ordinary Differential Equations
• Number Theory
• Probability

Select Browse, then select the course in which you are interested. You may select topics within that course.

Notes: Sequences and Series is part of One-Variable Calculus. We felt that since this topic had so many capsules associated with it, we wanted to introduce sub-topics. Also, the Number Theory collection of capsules does not correspond to a course in Course Communities, but has topics selected by the Editorial Board for Classroom Capsules and Notes.

New: The Mathematics of Planet Earth 2013 Collection is now available. These are articles published in the three journals of the MAA that are related to the Mathematics of Planet Earth 2013 theme.

## Featured Items

##### Solving the Noneuclidean Uniform Circular Motion Problem by Newton's Impact Method

The author uses Newtons impact method to compute the centripetal force exerted on a particle moving uniformly on a circumference of a noneuclidean circle.

##### Proof Without Words: Mengoli's Series

Mengolis Series is presented visually .

##### Interchanging Parameters of the Hypergeometric Distribution

A probabilistic explanation of a property of the hypergeometric distribution

##### Exactly When is $$(a+b)^n \equiv a^n + b^n$$ (mod $$n$$)

The congruence $$(a+b)^n \equiv a^n + b^n$$ (mod $$n$$) when $$n$$ is prime, or is a Carmichael number

##### The $$n$$th Derivative Test and Taylor Polynomials Crossing Graphs

The author describes $$n$$th derivative test, a generalization of 2nd derivative test, then applies it to give a quick proof of a condition for determining when the graph of a function and its Taylor polynomials intersect.

##### Application of the Lambert W Function to the SIR Epidemic Model

The author uses the Lambert W function to express the equilibrium solutions of the SIR epidemic model.