# 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

##### Lazy Student Integrals

The authors discuss ways to induce students to recognize the use of symmetry to evaluate challenging integrals, and to prevent student sidesteps.

##### Proof Without Words: A Graph Theoretic Decomposition of Binomial Coefficients

A visual binomial coefficient identity is presented.

##### Wronskian Harmony

The author obtains a closed form of the Wronskian for $$sin(kx)$$ and for $$e^{kx}, k=1,2,\ldots,n$$.

##### A Number-Theoretic Sum

The author presents a new Identity for integer functions and their inversion formulas.

##### Centroids Constructed Graphically

The authors "describe two different methods for locating the centroid of a finite number of given points ... without using coordinates or numerical calculations". Some examples are included.

##### Integrals of Products of Sine and Cosine with Different Arguments

Alternative method for integration of products of sines and cosines