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Functions Modeling Change:

A Preparation for Calculus,

Preliminary Edition

Eric Connally, Wellesley College, Deborah Hughes-Hallett, Harvard University, Andrew M. Gleason, Harvard University, et al.

624 Pages, Paper, ISBN: 0-471-17081-X, 1998

First Edition Available August, 1999, ISBN: 0-471-17084-4

This is the preliminary edition of a Precalculus text developed by the Consortium based at Harvard University and funded by a National Science Foundation Grant.

Functions Modeling Change can be used for precalculus courses, or possibly for courses in Algebra & Trigonometry. Students using this book should have successfully completed a course in intermediate algebra or high school algebra II. The book is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. Providing numerical and graphical approaches as well as the algebraic gives students another way of mastering the material. This approach encourages students to persist, thereby lowering failure rates.

A large number of the examples and problems provided in this innovative precalculus text are in the context of real-world problems which enable students to create mathematical models that will help them understand the world in which they live. Thus, the problem sets are not mirrors of the examples given in the text. Instead, non-routine problems are provided with the intention of establishing the idea that these types of problems are, in some sense, the real point of mathematics.

Features

The Rule of Four:
Each function is represented symbolically, numerically, graphically, and verbally.

The Way of Archimedes:
Formal definitions and procedures evolve from the investigation of practical problems.

Focuses on Fewer topics
than is customary, but each topic is treated in greater depth. Only those topics that are essential to the study of calculus are included.

Functions as models of change is the central theme.
This is based on the belief that the components of a next generation precalculus curriculum should be tied together by a clearly defined theme, with algebra developed as needed.

Allows for a broad range of teaching styles.
This text is flexible enough for use in large lecture halls, small classes, or in group or lab settings.

Reflects the spirit of the standards
established by the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC), and and meets the recommendations of the National Council of Teachers of Mathematics (NCTM)

Technology has a place in modern mathematics.
This text takes full advantage of technology when appropriate, although no specific technology is emphasized. It is important for students to learn how and when to use technology as a tool, as well as its limitations.

Changes from Draft Version to Preliminary Edition

The chapters have been reorganized to place each family of functions in a separate chapter where possible. The more theoretical material from Chapter 3 in the Draft Version has been moved to Chapters 4 and 7 in the Preliminary Edition so that students encounter the more abstract concepts later in the course. A new Chapter 6 includes new material on polar coordinates and vectors. New material on geometric series and parametric equations is included in a new Chapter 9. Many problems have been added, particularly easier ones, and the problems have been reordered for better grading.

Table of Contents:

Chapter 1: Functions: An Introduction

Sec 1: What is a Function?

Sec 2: Function Notation: Input and Output

Sec 3: Domain and Range

Sec 4: Working with Function Notation

Sec 5: Several Types of Functions

Sec 6: Rates of Change

Review Problems

Chapter 2: Linear Functions

Sec 1: What Makes a Function Linear?

Sec 2: Finding Formulas for Linear Functions

Sec 3: The Geometric Properties of Linear Functions

Sec 4: Fitting Linear Functions to Data

Review Problems

Chapter 3: Exponential and Logarithmic Functions

Sec 1: Introduction to the Family of Exponential Functions

Sec 2: More on Exponential Functions

Sec 3: Logarithms

Sec 4: Using Logarithms to Solve Exponential Equations

Sec 5: Applications of the Log Function

Sec 6: Models of Investment and the Number e

Sec 7: The Natural Logarithm Function

Sec 8: Fitting Curves to Data

Review Problems

Chapter 4: Transformations of Functions

Sec 1: Vertical and Horizontal Shifts of a Function's Graph

Sec 2: Reflections of a Function's Graph Across an Axis

Sec 3: Vertical Stretches of a Function's Graph

Sec 4: The Family of Quadratic Functions

Sec 5: Horizontal Stretches of a Function's Graph

Review Problems


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