Features of the Book:

Concept development flows from simple settings to general results

Differential Equations and integration are used to motivate and guide the
development of the concepts

Simple functions are used to approximate functions and antiderivatives.

The definite integral is defined using simple function approximation

The derivative form of the Fundamental Theorem of Calculus is proven rigorously
independent of the Mean Value Theorem.

Our approach allows Fourier Series to be included without adding to the
length or difficulty of a standard calculus course

Every group of four sections is devoted to a single main theme, which allows
instructors the freedom to design the course to suit their individual needs.

Themes are eventually developed graphically, numerically and analytically

Every fourth section is a "Pause" that reconsiders the material in the
previous three sections from a different perspective

The concepts introduced in each group of four sections are summarized in
a rigorous listing of key definitions and theorems after each "Pause".

After each summary, there is a selftest that allows the student to determine
how well they have acquired the material to that point

Individual sections are readable, thus permitting students to study calculus
by marking key ideas with a highlighter and making notes in the margins

Each section is written as a tutorial for the exercises that follow

Included in the exposition are short, simple exercises designed to reinforce
the reading. Thus, requiring the students to read the text involves little
more than assigning the intext exercises as part of the overall problem
set.

The intext exercises are simple enough to be answered orally, thus generating
class discussion and providing a tool for designing lectures.

The use of technology is carefully interwoven into topics where it is either
a tool widely used by scientists, mathematicians or engineers, or where
it aids in the discovery or comprehension of a concept.

Data sets and simple curvefitting are incorporated throughout the textbook

The graded problem sets drill the techniques encountered in the section,
whether they are graphical, numerical or analytical.

Applications are developed from a mathematical viewpoint with references
to other fields so that they do not seem contrived and out of context.

The Next Step sections are short essays that elaborate on themes
introduced in the text. The AWrite
to Learn@ assignments that follow
afford the student an opportunity to learn through writing and to develop
technical writing skills.

Advanced contexts and indepth exercises are included at the end of the
"Next Steps" as a tool to challenge better students.

The quotient rule is introduced a section after the product rule so that
students do not confuse the signs of the two.

Proofs are included for all the theorems except for the Mean Value Theorem
(Because an actual proof of the Mean Value Theorem requires the HeineBorel
theorem or its equivalent, it is developed intuitively and without proof).
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