*
Janet Beery, University of
Redlands*

These classroom
explorations and exercise sets are designed to help students discover and/or
understand important ideas and techniques from calculus. They assume students
have access to a graphing calculator or computer grapher but not necessarily to
a computer algebra system (CAS). I use them with the calculus text by
Hughes-Hallett, et al, published by Wiley, and have listed corresponding section
numbers from the 4^{th} and 5^{th} editions of this text. These
are listed as (4^{th} / 5^{th}) where they differ.

Riding the Calculus
Bus: Velocities as Limits (2.1)

Slopes as Limits (2.2)

Derivatives as Limits (2.2,
2.3)

Derivatives as Slopes (2.3,
preview of graphing and optimization strategies in Chapter 4)

Concavity and First and
Second Derivatives (2.5)

Derivatives and Smooth Airplane
Take-off (2.6, 3.1)*

Tests for Local
Extrema and Concavity (4.1)

Review of Tests for
Local Extrema and Concavity (4.1)

Candidates Test for
Global Extrema (4.3 / 4.2)

Tests for Global Extrema
(4.3, 4.5 / 4.2, 4.4)

Optimization without
Calculus (4.3, 4.5 / 4.2, 4.4)

Optimization with Calculus
(4.5 / 4.4)

More Optimization (4.5 /
4.4)

Riding the Calculus Bus: Distances as Areas and Limits (5.1, 7.5)

For introducing the definite integral (Chapter 5) and antiderivatives (Chapter
6): various explorations from Paul Foerster’s *Calculus Explorations,* Key
Curriculum Press, 1998, especially Exploration 3, Introduction to Definite
Integrals, and Exploration 26, A Motion Antiderivative Problem

Modeling the Flight of a Water Balloon
(6.3)

Another Fundamental Theorem of
Calculus! (6.4)

The Most Ubiquitous Initial Value
Problems (11.1)

Population and Food (11.5)

World Population Models
(11.7)*

* I rarely have time to use this exploration, but I included it because I sure wish I did!