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Quantitive Reasoning & the Environment

By Greg Langkamp, Joseph Hull

Published by Pearson

Published Date: Jul 10, 2006

Table of Contents

Part 1: Essential Numeracy

Chapter 1: Measurement and Units

Mercury and the Inuit of Greenland

Measuring

Accuracy and Precision of Measurement

Estimation and Approximation

Units of Measurement

Unit Conversion

Compound Units

Units in Equations and Formulas

Unit Prefixes

Scientific Notation and Order of Magnitude

Powers of 10 and Logarithms

Logarithmic Scales

Chapter Summary

End-of-Chapter Exercises

Science in Depth:  Global Warming

Chapter Project: Melting of the Ice Caps

    (all projects posted at enviromath.com)

 

Chapter 2: Ratios and Percentages

Ratios

Normalization

Percentage as a Type of Ratio

Parts per Thousand

Parts per Million and Parts per Billion

Percentage as a Measure of Change

Percentage Difference and Percentage Error

Proportions

Probability

Recurrence Interval

Chapter Summary

End-of-Chapter Exercises

Science in Depth:  Sinkholes and Lakes

Chapter Project: Measuring Habitat of Florida Lakes

 

Chapter 3: Charts and Graphs

Pie Charts

Bar Charts

Frequency Histograms

Using Technology: Histograms

Relative Frequency Histograms

Scatterplots

Using Technology: Scatterplots

Line Graphs

Chapter Summary

End-of-Chapter Exercises

Science in Depth: Energy Demand and the Arctic National Wildlife Refuge

Chapter Project: U.S. Energy Flows

 

Part 2: Function Modeling

Chapter 4: Linear Functions and Regression

Modeling with Linear Functions

Units of Measure in Linear Equations

Dependent versus Independent Variables

Graphing Linear Equations

Using Technology: Graphs and Tables

Approximating Almost-Linear Data Sets

    straightedge method

    least squares regression

Using Technology: Linear Regression

The Correlation Coefficient "r"

Using Technology: The Correlation Coefficient 

Correlation Fallacies

Chapter Summary

End-of-Chapter Exercises

Science in Depth:  Population Growth

Chapter Project: Fertility Rates in Developing Countries

 

Chapter 5: Exponential Functions and Regression

Exponential Rates and Multipliers

The General Exponential Model

Finding Exponential Functions–the More General Case

Solving Exponential Equations

Doubling Times and Half-Lives

Approximating Almost-Exponential Data Sets

    straightedge method

    least squares regression

Using Technology: Exponential Regression

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Chicken Nation

Chapter Project: Broiler Chicken Production in the United States

 

Chapter 6: Power Functions

Basic Power Functions

Solving Power Equations

Approximating Power-Like Data Sets

    straightedge method

    least squares regression

Using Technology: Power Regression

Power Law Frequency Distributions

Power Law Distributions and Fractals

Recurrence Intervals

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Earthquakes and Fractals

Chapter Project: A New Model for Earthquakes

 

Part 3: Difference Equation Modeling

Chapter 7: Introduction to Difference Equations

Sequences and Notation

Modeling with Difference Equations

    Linear Difference Equations

    Exponential Difference Equations

Why Use Difference Equations?

Affine Difference Equations

Using Technology: Difference Equations

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  The Politics of Immigration

Chapter Project: Human Population and Migration

 

Chapter 8: Affine Solution Equations and Equilibrium Values

The Solution Equation to the Affine Model

Equilibrium Values

Classification of Equilibrium values

Revisiting the Affine Solution Equation 

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Get The Lead Out

Chapter Project: Lead in the Body

 

Chapter 9: Logistic Growth, Harvesting and Chaos

Modeling Logistic Growth with Difference Equations

Logistic Equilibrium Values

Harvest Models 

Periodic Behavior

Chaotic Behavior

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Harvesting and Sustainable Forestry

Chapter Project: Harvesting and Sustainability

 

Chapter 10: Systems of Difference Equations

Systems Modeling

Using Technology: Systems of Difference Equations

Exponential Change and Stable Age Distributions

What Else Besides Populations?

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  A River Runs Through Europe

Chapter Project: Water Pollution in a System of Lakes

 

Part 4: Elementary Statistics

Chapter 11: Fundamentals of Statistics

Measures of Center and Other Descriptive Statistics

Weighted Means

Quartiles and the 5 Number Summary

Boxplots

Using Technology: Finding Descriptive Statistics

Shape of a Data Set

Using Technology: Histograms

A Skew Formula

Comparing the Mean and Median

Sampling

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Energy Makeover

Chapter Projects: Electric Bills and Super Bulbs

 

Chapter 12: Standard Deviation

Standard Deviation

Calculating Position Using Z-scores

Outliers

Chebychev's Rule

Normal Distributions

The Empirical Rule

Chapter Summary 

End-of-Chapter Exercises

Science in Depth: Impermeable Surfaces and Urban Runoff

Chapter Projects: Urban Runoff Index

 

Chapter 13: Normal Distributions

The Standard Normal Distribution

Transformations to Normal 

Confidence Intervals

Chapter Summary 

End-of-Chapter Exercises

Science in Depth:  Hazardous Household Waste

Chapter Project: Hazardous Waste Generation and Monetary Disincentives

 

Appendix: Common Units of Measurement

Solutions to Odd Exercises

Index

Print

Quantitive Reasoning & the Environment

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