# 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

##### A Classroom Approach to Involutions

Elementary examples from college algebra illustrate the idea of involutions.

##### Applications of Transformations to Numerical Integration

The authors discuss the evaluation of certain improper integrals by first transforming them.

##### Bernstein's Examples on Independent Events

When the sample space is too small, then Bernstein's examples on independent events fail.

##### On the Sum of Consecutive $$K$$th Powers

The author provides a direct and elementary proof of the Bernoulli formula for the sum of consecutive $$K$$th powers.

##### Power Series Expansions for Trigonometric Functions via Solutions to Initial Value Problems

Using initial value problem with repeated differentiations, the author obtains the complicated coefficients of the power series for powers of the secant function.

##### Dogs Don't Need Calculus

The authors use inequalities to solve optimization problems without resorting to calculus, as illustrated by four common examples in calculus.