Contents
Prologue: Calculator arithmetic i
Preface v
Preface v
Typing mathematical expressions 1
Rounding 1
Scientific notation 3
Parentheses and grouping 4
Minus signs 6
Special numbers and e 8
Chain calculations 9
1 Functions 17
1.1 Functions given by formulas 17
Functions of one variable 17
Functions of several variables 18
1.2 Functions given by tables 27
Reading tables of values 27
Filling gaps by averaging 27
Average rates of change 28
Spotting trends 30
1.3 Functions given by graphs 37
Reading graphs 37
Filling graphs by averaging 28
Average rates of change 30
Spotting Trends 30
1.4 Functions given by words 53
Comparing formulas and words 53
Getting formulas from words 56
Proportion 59
2 Graphical and tabular analysis 67
2.1 Tables and trends 67
Getting tables from formulas 67
Optimizing with tables of values 73
2.2 Graphs 83
Hand-drawn graphs from formulas 83
Graphing with the calculator 84
Tracing the graph 84
Choosing a viewing window in practical settings 86
Getting limiting values from graphs 91
2.3 Solving linear equations 99
The basic operations 99
Reversing the roles of variables 101
2.4 Solving nonlinear equations 111
2.5 Optimization 123
3 Straight lines and linear functions 136
3.1 The geometry of lines 136
Characterizations of straight lines 136
The slope of a line 139
Getting slope from points 140
3.2 Linear functions 145
Constant rates of change 145
Linear functions and straight lines 147
Linear equations from data 151
3.3 Modeling data with linear functions 159
Testing data for linearity 159
3.4 Linear Regression 169
3.5 Systems of equations 181
Graphical Solutions of systems and equations 181
Algebraic solutions 186
4 Exponential functions 191
4.1 Exponential growth and decay 191
Exponential growth 191
Exponential decay 192
Constant proportional change 196
Unit conversion 199
Exponential functions and daily experience 201
4.2 Modeling exponential data 207
Recognizing exponential data 207
Constructing an exponential model 208
Growth and decay factor units in exponential modeling 212
4.3 Modeling nearly exponential data 219
From linear to exponential data 219
From exponential to linear data; the logarithm 221
Exponential regression 223
A note about continuous growth 230
5 Rates of Change 235
5.1 Velocity 235
5.2 Rates of change for other functions 251
Examples of rates of change 251
Common properties of all rates of change 252
When the rate of change is zero 255
When the rate of change is constant 257
5.3 Equations of change: linear and exponential functions revisited 263
Equation of change for linear functions 263
Equation of change for exponential functions 265
Why equations of change ? 268
5.4 Equations of change: Graphical solutions 273
Equilibrium solutions 273
Sketching graphs 289
5.5 Estimating rates of change 289
Rates of change for tabulated data 289
Rates of change for functions given by formulas 292
6 Mathematics of Ecology 299
6.1 Population Dynamics: Exponential Growth 299
6.2 Population Dynamics: Logistic Growth 313
6.3 Survivorship curves 327
6.4 Power functions and patterns in ecology 339
Brief answers to odd numbered exercises 357