Functioning in the Real World: A
Precalculus Experience, Second Edition
by Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker,
and Martha J. Siegel (Pearson Addison Wesley) is a text designed to prepare
students for calculus with a focus on ideas and reasoning, manipulation and
decision-making.
Both cases illustrate themes
that run through
Functioning in the Real World. The authors focus on the applications of
mathematics to situations all around us and on the function concept that allows
us to study these phenomena. In
Functioning in the Real World students learn to use a combination of
algebraic, graphical, and numerical methods, depending on which is the most
helpful tool in any given context.
The mathematics curriculum is
in the process of change to establish a better balance among geometric,
numerical, symbolic, and verbal approaches. There is a much greater emphasis on
understanding fundamental mathematical concepts, on realistic applications, on
the use of technology, on student projects, and on more active learning
environments. These approaches tend to make greater intellectual demands on the
students compared to traditional courses that place heavy emphasis on rote
memorization and manipulation of formulas.
Led by authors,
Sheldon P. Gordon, Farmingdale State University of New York; Florence S. Gordon,
New York Institute of Technology; Alan C. Tucker, SUNY at Stony Brook; and
Martha J. Siegel, Towson State University, and with support from the
National Science Foundation, the Math Modeling/ PreCalculus Reform Project
developed a new precalculus or college algebra/ trigonometry experience with the
following goals:
To accomplish these goals, the
authors have adopted several basic principles advocated by most leading
mathematics educators.
The second edition contains a
wealth of new applications, examples and problems, and all real-world data sets
have been updated. All concepts and methods are approached using the Rule of
Three: graphically, symbolically, and numerically.
The new edition has been
reorganized and completely rewritten to provide a slower pace through topics
that some students find challenging. It also contains a more prominent role for
algebraic topics, where the algebraic steps involved in derivations are now
highlighted to assist students who may have forgotten some of the algebra they
learned in prior courses. Many of the problem sets now include collections of
problems, called Exercising Your Algebra Skills, to give those students who need
it some practice with routine algebra. The book also includes a considerably
expanded treatment of trigonometry and the use of the trig functions as models
of periodic behavior; there are now three chapters devoted to these ideas and
methods.
Major changes in the second
edition include:
Chapter 2: Families of
Functions
The long section on linear
function has been split into two shorter sections to slow the pace. Similarly,
the treatment of exponential functions has been slowed by presenting the
material in two sections, one on exponential growth functions and the other on
exponential decay functions.
Chapter 3: Fitting Functions
to Data
Many new examples, particularly
relating to power functions, have been added and considerably more emphasis has
been placed on the judgmental issues and mathematical reasoning. A new optional
section on multivariable linear regression has been added.
Chapter 4: Extended Families
of Functions
The material has been
reorganized to bring together all the discussions related to polynomial
functions. New sections have been added that relate the ideas on shifting and
stretching functions to operations on tables of data. A new section has been
added on the logistic and surge functions as applications of the material on
building new functions from old.
Chapter 5: Modeling with
Difference Equations
The introduction to difference
equation models has been totally rewritten and reorganized. The more challenging
material has been moved to Chapter 12.
Chapter 6: Introduction to
Trigonometry
A new chapter on right angle
trigonometry has been written for those students who need an exposure to this
material. The development starts with the tangent ratio. The chapter includes
the law of sines and the law of cosines.
Chapter 7: Modeling Periodic
Behavior
This chapter presents the use
of the trigonometric functions as models for periodic behavior.
Chapter 8: More About the
Trigonometric Functions
This chapter presents more
advanced ideas on the trigonometric functions, especially trigonometric
identities, complex numbers and DeMoivre's theorem.
Chapter 9: Geometric Models
The material on the conic
sections has been split into several sections. Additional applications of the
hyperbola have been added.
Chapter 10: Matrix Algebra
and its Applications
A new section introducing
geometric and physical vectors has been added. Additional examples and problems
have been added that link matrix methods more directly to previous topics in the
book.
Chapter 11: Probability
Models
All of the material on
probability models, which had been scattered throughout the text, has been
collected into this chapter. A new section introducing the normal distribution
and its uses has been added and made available for downloading off the web at
www.aw.com/ggts
as supplemental material.
Chapter 12: More About
Difference Equations
The more sophisticated ideas
and methods on difference equations have been combined into this chapter.
Moreover, additional sections have been added introducing several models based
on systems of difference equations; these include the predator-prey model and a
model for competitive species. This supplementary chapter is available on the
website.
Functioning in the Real World is approprate for use as an alternative
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