What This Book is About [ Top ]
This book presents a fresh, new approach to the concepts of calculus for students
in fields such as business, economics, liberal arts, management, and the social and
life sciences. It is appropriate for two-semester courses generally known as "brief
calculus" or "applied calculus."
Philosophy [ Top ]
Our overall goal is to improve learning of basic calculus concepts by involving
students with new material in a way that is significantly different from traditional
practice. The development of conceptual understanding, not mastery of algebraic skill
and technique, is our guiding force coupled with a commitment to make calculus meaningful
to the student. Thus, the material in this book is data-driven and technology-based,
with a unique modeling approach. It considers the ability to correctly interpret
the mathematics of real-life situations of equal importance to the understanding
of the concepts of calculus in the context of change.
Data-Driven [ Top ]
Many everyday, real-life situations involving change are discrete in nature and
manifest themselves through data. Such situations often can be represented by continuous
or piecewise continuous mathematical models so that the concepts, methods, and techniques
of calculus can be brought to light. Thus we seek, when appropriate, to make real-life
data a starting point for our investigations.
The use of real data and the search for appropriate models also exposes the students
to the reality of uncertainty. We emphasize that sometimes there can be more than
one appropriate model and that answers derived from models are only approximations.
We believe that exposure to the possibility of more than one correct approach or
answer is valuable.
Technology-Based [ Top ]
Calculus has traditionally relied upon a high level of algebraic manipulation.
However, many non-technical students are not strong in algebraic skills, and an algebra-based
approach tends to overwhelm them and stifle their progress. Today's easy access to
technology in the form of graphing calculators and microcomputers breaks down barriers
to learning imposed by the traditional reliance on algebraic methods. It creates
new opportunities for learning through graphical and numerical representations. We
welcome these opportunities in this book by assuming continual and immediate access
This book requires that students use graphical representations (scatter plots
of data and graphs of functions) freely, make numerical calculations routinely, and
fit functions to data. Thus, continual and immediate access to technology is absolutely
essential. Because of their low cost, portability, and ability to personalize the
mathematics, the authors prefer graphing calculators. These materials have also been
successfully taught using microcomputer software (such as Maple) and are appropriate
for use with spreadsheets.
It is worth noting that different technologies may give different model coefficients
than those given in this book. We used a TI-83 graphing calculator to generate the
models in the text and the answer key. Other technologies may use different fit criteria
for some models than the criteria used by the TI-83.
Modeling Approach [ Top ]
We believe that modeling is an important tool and introduce it at the outset.
Both linear and nonlinear models of discrete data are used to obtain functional relationships
between the variables of interest. The functions given by the models are the ones
used by students to conduct their investigations of calculus concepts. It is the
connection to real-life data that most students feel shows the relevance of the mathematics
in this course to their lives and adds reality to the topics studied.
Interpretation Emphasis [ Top ]
This book is substantially different from traditional texts, not only in the philosophy
but also in its overall focus, level of activities, development of topics and attention
to details. Interpretation of results is a key feature of this text that allows students
to make sense of their mathematical concepts and appreciate the usefulness of those
concepts in their lives.
Informal Style [ Top ]
While we appreciate the formality and precision of mathematics, we also recognize
that this alone can deter students from access to mathematics. Thus, we have sought
to make our presentations as informal as possible by using non-technical terminology
where appropriate and a conversational style of presentation.
Projects [ Top ]
Projects included after each chapter are intended to be group projects with oral
and/or written presentations. We recognize the importance of helping students develop
the ability to work in groups, as well as hone presentation skills. The projects
also give opportunity for students to practice the kind of writing that they will
likely have to do in their future careers.
Other Pedagogical Features [ Top ]
Each chapter opens with a real-life situation and several questions about the
situation that relate to the key concepts in the chapter.
A Concept Inventory is listed at the end of each section, giving students a brief
summary of the major ideas developed in that section.
The Section Activities begin by cementing concepts followed by explorations of
topics using, for the most part, actual data in a variety of real-world settings.
Questions and interpretations pertinent to the data and the concepts are always included
in these activities. The activities do not mimic the examples in the chapter discussion
and thus require more independent thinking on the part of the students. Possible
answers to odd activities are given at the end of the book.
A Chapter Summary connects the results of the chapter topics and further emphasizes
the importance of knowing these results.
Chapter Review Test
A Chapter Review Test at the end of each chapter provides practice with techniques
and concepts. Answers to the Chapter Review Test are included in the answer key.
Supplements [ Top ]
The Instructor's Guide gives practical suggestions for using the text in the matter
intended by the authors. It contains sample tests, ideas for in-class group work,
suggestions for implementing and grading projects, and complete activity solutions.
The technology supplements provide technology-specific instructions ordered to
match the organization of the text chapters. An open-book icon appears at places
in the text where a new concept or skill is presented in the technology supplements.
A Student Solutions Guide is also available. A Test Item File is available in
PC and Macintosh formats.