Functioning in the Real World: A Precalculus Experience

by Gordon, Sheldon P.; Gordon, Florence S.; Fusaro, B. A.; Siegel, Martha J.; Tucker, Alan C.

• ISBN13: 9780201846287
• ISBN10: 0201846284
• Format: Hardcover
• Copyright: 1996-11-01
• Publisher: Pearson College Div

Summary

Functioning in the Real World contains the course material that grew out of the mathematical Modeling/Precalculus Reform Project, which received major funding from NSF. This text seeks to prepare and motivate students for mastering the new generation of calculus courses, and offers a dramatically different alternative to standard Precalculus and College Algebra and Trigonometry texts. The goal of the text is to emphasize the qualitative, geometric and computational aspects of mathematics, within a framework of mathematical modeling at a level appropriate to precalculus students. It capitalizes on the fact that most students are more interested in applications of mathematics than in theory. Consequently, applications drive all the mathematical development, making the topics more accessible to students who may not have experienced success in mathematics.

Table of Contents

(Each Chapter ends with a Summary and Review.)

Functions in the Real World

Functions are all around us

Describing the behavior of functions

Representing functions symbolically

Connecting geometric and symbolic representations

Mathematical models

Families of Functions

Introduction

Linear functions

Linear functions and Data

Exponential growth functions

Exponential decay functions

Logarithmic functions

Power functions

Comparing Rates of Growth and Decay

Inverse functions

Fitting Functions to Data

Introduction to Data Analysis

Linear regression analysis

Fitting nonlinear functions to data

How to fit exponential and logarithmic functions to data

How to fit power functions to data

How good is the fit? Linear models with several variables

Extended Families of Functions

Introduction to polynomial functions

The behavior of polynomial functions

Modeling with polynomial functions

The roots of polynomial equations: Real or complex? Finding polynomial patterns

Building new functions from old: Operations on Functions

Building new functions from old: Shifting, stretching, and shrinking

Using shifting and stretching to analyze data

The logistic and surge functions

Modeling with Difference Equations

Eliminating drugs from the body

Modeling with difference equations

The logistic or inhibited growth model

Newton's Laws of Cooling and Heating

Geometric sequences and their sums

Introduction to Trigonometry

The tangent of an angle

The sine and cosine of an angle

The sine, cosine and tangent in general

Relationships among trigonometric functions

The law of sines and the law of cosnes

Modeling Periodic Behavior

Introduction to the sine and cosine functions

Modeling periodic behavior with sine and cosine

Solving equations with sine and cosine

The inverse functions

The tangent function

More About the Trigonometric Functions

Relationships among trigonometric functions

Approximating sine and cosine with polynomials

Properties of complex numbers

The road to chaos

Geometric Models

Introduction to coordinate systems

Analytic geometry

Conic sections

The Ellipse

Conic sections

The Hyperbola and the Parabola

Parametric curves

The polar coordinate system

Families of curves in polar coordinates

Matrix Algebra and Its Applications

Geometric vectors

Linear models

Scalar products

Matrix multiplication

Gaussian elimination

Probability Models (online only)

Introduction to probability models

Binomial probability and the binomial formula

Using probability to investigate polynomials

Geometric probability

Estimating areas of plane regions

The normal distribution function

Waiting time at a red light

Random patterns in chaos

More About Difference Equations (online only)

Solutions of difference equations

Constructing solutions of first order difference equations

Modeling with first order, non-homogeneous difference equations

Financing a car or a home

Solving the Fibonacci and other second order difference equations

The predator-prey model

Competing species

Iteration and chaos

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