ix
Moreover, this approach is consistent with the following goals:
• To have students engage in an active, inquiry-driven approach, where learners strive
to construct solutions and approaches to ideas on their own, with appropriate
support through questions posed, hints, and guidance from the instructor and text.
• To build in students intuition for why the main ideas in calculus are natural and
true. Often, we do this through consideration of the instantaneous position and
velocity of a moving object, a scenario that is common and familiar.
• To challenge students to acquire deep, personal understanding of calculus through
reading the text and completing preview activities on their own, through working on
activities in small groups in class, and through doing substantial exercises outside of
class time.
• To strengthen students’ written and oral communicating skills by having them write
about and explain aloud the key ideas of calculus.
Features of the Text
Instructors and students alike will find several consistent features in the presentation,
including:
• Motivating Questions. At the start of each section, we list 2-3 motivating questions
that provide motivation for why the following material is of interest to us. One goal
of each section is to answer each of the motivating questions.
• Preview Activities. Each section of the text begins with a short introduction,
followed by a preview activity. This brief reading and the preview activity are
designed to foreshadow the upcoming ideas in the remainder of the section; both
the reading and preview activity are intended to be accessible to students in advance
of class, and indeed to be completed by students before a day on which a particular
section is to be considered.
• Activities. A typical section in the text has three activities. These are designed
to engage students in an inquiry-based style that encourages them to construct
solutions to key examples on their own, working individually or in small groups.
• Exercises. There are dozens of calculus texts with (collectively) tens of thousands
of exercises. Rather than repeat standard and routine exercises in this text, we
recommend the use of WeBWorK with its access to the National Problem Library
and around 20,000 calculus problems. In this text, there are approximately four
challenging exercises per section. Almost every such exercise has multiple parts,
requires the student to connect several key ideas, and expects that the student
Moreover, this approach is consistent with the following goals:
• To have students engage in an active, inquiry-driven approach, where learners strive
to construct solutions and approaches to ideas on their own, with appropriate
support through questions posed, hints, and guidance from the instructor and text.
• To build in students intuition for why the main ideas in calculus are natural and
true. Often, we do this through consideration of the instantaneous position and
velocity of a moving object, a scenario that is common and familiar.
• To challenge students to acquire deep, personal understanding of calculus through
reading the text and completing preview activities on their own, through working on
activities in small groups in class, and through doing substantial exercises outside of
class time.
• To strengthen students’ written and oral communicating skills by having them write
about and explain aloud the key ideas of calculus.
Features of the Text
Instructors and students alike will find several consistent features in the presentation,
including:
• Motivating Questions. At the start of each section, we list 2-3 motivating questions
that provide motivation for why the following material is of interest to us. One goal
of each section is to answer each of the motivating questions.
• Preview Activities. Each section of the text begins with a short introduction,
followed by a preview activity. This brief reading and the preview activity are
designed to foreshadow the upcoming ideas in the remainder of the section; both
the reading and preview activity are intended to be accessible to students in advance
of class, and indeed to be completed by students before a day on which a particular
section is to be considered.
• Activities. A typical section in the text has three activities. These are designed
to engage students in an inquiry-based style that encourages them to construct
solutions to key examples on their own, working individually or in small groups.
• Exercises. There are dozens of calculus texts with (collectively) tens of thousands
of exercises. Rather than repeat standard and routine exercises in this text, we
recommend the use of WeBWorK with its access to the National Problem Library
and around 20,000 calculus problems. In this text, there are approximately four
challenging exercises per section. Almost every such exercise has multiple parts,
requires the student to connect several key ideas, and expects that the student