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Tables of Contents for College Mathematics Through Applications
Chapter/Section Title
Page #
Page Count
Preface
xv
 
Linear Equations
0
62
The Mathematical Crystal Ball
2
4
Take a Walk with the CBL
6
4
Looking at the Data
8
2
Distance, Time, and Two Kinds of Rate
10
7
Velocity and Speed
10
7
Equation of a Line: Slope and y-Intercept
17
16
Slope of a Straight Line
18
1
Applications of Slope
19
4
Intercepts of a Graph
23
2
Fitting a Line to the Data---The Slope-Intercept Form of the Line
25
3
The Constant Velocity Equation
28
5
Three More Forms of the Linear Equation
33
16
Using the Slope and a Point
34
1
Using Two Points
35
1
Using the Angle of the Line
36
5
Decimal Precision and Decimal Accuracy
41
8
A Linear Model That Uses All the Points
49
13
Fitting a Regression Line to Data
51
6
Summary and Review
57
3
Test
60
2
Quadratic Functions
62
60
The Bouncing Ball
64
1
Velocity That Varies
65
5
Graphs That Tell a Story
65
1
Average Speed and Average Velocity
66
4
Follow the Bouncing Ball
70
5
CBL and the Bouncing Ball
70
2
Looking at One Bounce
72
1
Quadratic Regression
73
1
Thinking about Quadratic Regression
74
1
Introduction to Functions
75
8
Introduction to Functions
75
2
Naming a Function
77
2
How Functions Are Defined
79
1
Graphing Functions
80
1
Looking More Closely at a Graph
81
2
Working with Parabolas
83
14
Roots of a Quadratic Function
83
1
Roots and Factors
84
6
Maximum or Minimum of a Quadratic Function
90
1
Graphs of Quadratic Functions
91
2
Approximating Real Roots of Any Function
93
4
Projectile Motion
97
11
A Falling Object
97
2
Transforming Data
99
1
Giving it a Toss
100
2
Comparing Transformed Graphs
102
1
Another Look at Coefficients a and b
102
2
Thinking about the Quadratic Model
104
4
Velocity at an Instant
108
14
Return to the Bouncing Ball
115
2
Summary and Review
117
2
Test
119
3
Models of Periodic Data: Introducing Trigonometry
122
96
Analyzing the Touchtone Phone
124
1
Introduction to the Trigonometric Functions
125
12
Definitions of the Trigonometric Functions
126
1
Calculations with Triangles
127
10
Graphs of Trigonometric Functions
137
16
Angles Larger than 90°
137
4
Drawing the Graphs
141
1
The Peculiar Tangent Function
142
2
Negative Angles and Other Strange Things
144
4
Modeling Alternating Currents
148
1
Modeling Vibrations and Sound Waves
149
4
Period, Amplitude, Frequency, and Roots
153
17
Cycle and Period
153
3
Frequency
156
1
Amplitude
157
5
Solving Trigonometric Equations
162
5
Roots of Trigonometric Functions
167
3
Vertical and Horizontal Translations
170
12
Vertical Shifts or Translations of Functions
171
1
Phase Shift
172
1
Horizontal Shifts or Translations of Functions
173
6
Fitting Trigonometric Functions to Periodic Data
179
3
Modeling With Radian Measure
182
13
Radians and Degrees
182
4
Modeling the Motion of a Spring
186
3
Modeling Sounds and Music
189
6
Modeling Wave Combinations
195
23
More about Alternating Current
195
2
Alternating Current and the Addition of Trigonometric Functions
197
1
Combining Waves of Different Frequency
198
4
Modeling Musical Notes and Chords
202
10
Summary and Review
212
4
Test
216
2
Mathematical Models in Geometry: Images in Two and Three Dimensions
218
74
What's the Best Shape?
220
2
Volume and Surface Area
222
14
Volume
222
3
Surface Area
225
2
Exploring Max/Min Problems
227
4
First Attempt at the Minimum Area of a Cylinder
231
5
Triangles Are Everywhere
236
17
Why Is the Area of a Triangle Half the Base x Height?
237
1
Trigonometry and the Areas of Triangles
238
2
The Law of Sines
240
4
The Pythagorean Theorem
244
2
Distance on a Graph
246
2
The Law of Cosines
248
5
Pythagorean Theorem and Circles
253
13
Definition of a Circle and Some of Its Parts
254
3
Circles Not Centered at the Origin
257
1
Pythagorean Trigonometry Identities
258
2
Circumference and Area of a Circle
260
6
Definition and Use of Radians
266
12
Radians
266
4
Sectors and Arcs of Circles
270
2
Summary of Differences: Radians vs. Degrees
272
1
Moving in Circles
272
6
Prisms, Pyramids, and Other 3-D Figures
278
14
Prisms
278
1
Pyramids
278
2
Cylinders
280
1
Cones
281
1
Solution of the Chapter Project's Cylinder Problem
282
5
Summary and Review
287
3
Test
290
2
Modeling Motion in Two Dimensions
292
82
What's the Best Angle?
294
1
Prlimary Analysis
294
3
Flight Trajectories
297
8
Looking at Trajectories
297
1
Vectors and the Components of Velocity
297
3
The Influence of Gravity
300
5
Parametric Equations
305
16
Graphing Parametric Equations
306
2
Trigonometry, Circles, and Parametric Equations
308
2
Parametric Equations of Ellipses
310
2
Plotting Planetary Trajectories
312
2
Modeling Planetary Velocity
314
1
Modeling Other Gravity-Influenced Trajectories
315
6
Vectors
321
18
Vectors in Navigation
321
2
Modeling Vector Sums with Triangles
323
2
Modeling Vector Sums with Parallelograms
325
5
Vectors and Gravity: Motion on a Ramp
330
2
Modeling Impedance in RC Circuits
332
7
Vectors and Complex Numbers
339
20
Types of Numbers
339
5
Imaginary Numbers
344
4
Arithmetic of Complex Numbers
348
2
Geometry of Complex Numbers
350
4
Polar Form for a Complex Number
354
3
Phasors and Complex Numbers
357
2
Solving the Best-Angle Problem
359
15
Solution That Uses Algebra and Trigonometry
363
1
What If the Beginning and Ending Heights Are Different
364
3
Summary and Review
367
4
Test
371
3
Polar Graphing and Elementary Programming
374
66
Programming a Robot Arm
376
2
Review of Two-Dimensional Graphing
378
11
Connecting Cartesian and Parametric Graphing
378
7
Parametric Equations and the Oscilloscope
385
2
Lissajous Curves
387
2
Polar Coordinates
389
15
Plotting Points in Polar Coordinates
389
1
Plotting Polar Equations
390
6
Patterns in Polar Graphs
396
1
Patterns in Roses and Their Relatives
397
2
Connecting Polar and Rectangular Equations
399
5
Applications of Polar Graphing: Ellipses
404
12
Ellipses and Eccentricity
404
3
Plotting Orbits of Comets
407
1
Polar Equations of Ellipses
408
2
Other Applications of Ellipses
410
6
Understanding TI-83 Programs
416
5
Introduction to TI-83 Programming
417
2
How the Program XYGRABBR Works
419
2
Writing TI-83 Programs
421
7
Entering a Program
421
2
Editing an Existing Program
423
5
Solving the Chapter Project
428
12
Plotting Curves One Point at a Time
428
3
Plotting Connected Curves
431
5
Summary and Review
436
2
Test
438
2
Modeling With Sequences and Series
440
100
Estimating Cross-Sectional Areas
442
1
Preliminary Analysis
442
4
Sequences
446
15
Defining Sequences Directly
447
7
Defining Sequences Recursively
454
7
Limits of Sequences
461
11
Sequences and Chaos Theory
465
1
A Sequence of Areas
466
6
Looking More Closely at Limits
472
12
Three Important Sequences
472
5
The Algebra of Limits
477
7
Applications of Geometric Sequences
484
25
Interest on a Savings Account
484
7
Bouncing Ball
491
3
Charing and Discharging a Capacitor
494
5
Radioactivity and Half-Life
499
3
Exponents and Notes in a Musical Scale
502
2
Negative, Zero, and Fractional Exponents
504
5
Arithmetic and Geometric Series
509
13
A Legendary Bonus
510
4
Limits of Geometric Series
514
4
Charging a Capacitor
518
2
Arithmetic Series
520
2
Estimating Areas under Curves
522
18
Riemann Sums
523
2
Estimation with Middle Rectangles
525
3
A Program to Estimate Areas
528
2
How the Program Works
530
4
Summary and Review
534
4
Test
538
2
Modeling With Algebraic Functions
540
92
Seismographs and Pendulums
542
1
Preliminary Analysis
542
5
Power Functions: f (x) = kxn
547
14
Algebraic Functions
548
2
Exploring the Graphs of f (x) = kxn
550
7
Summary: Shapes of Power Function Graphs
557
4
Variation and Power Functions
561
14
A Legend about Gifts and Gold
562
1
Direct Variation
562
4
Variation of Light Intensity with Distance
566
2
Inverse Variation
568
7
Polynomial Functions
575
9
Roots of Polynomials
576
2
Factored Form of a Polynomial
578
1
Limits and Graphs of Polynomial Functions
579
5
Application of Polynomials
584
11
How do Calculators Compute Trigonometric Values?
584
2
The nth Term of a Sequence
586
9
Patterns in Slopes of Power Functions
595
11
Plotting a Tangent to a Curve
597
4
A Program that Draws Tangents
601
1
Modeling the Slope Function
602
4
Analyzing Rational Functions
606
16
Shifted Forms of Power Functions
606
8
Variations on Familiar Functions
614
4
Solving a Light Intensity Problem with Graph, Table, and Algebra
618
4
Solving the Chapter Project
622
10
Summary and Review
626
4
Test
630
2
Exponential and Logarithmic Functions
632
64
Modeling Temperature Changes
634
1
Preliminary Analysis
634
4
Exponential Functions
638
6
Graphs of Exponential Functions
640
2
Intercepts and Asymptotes in Exponential Functions
642
2
Logarithms and Inverse Functions
644
14
What Are Logarithms?
644
3
Properties of Logarithms
647
4
Why Study Logarithms?
651
3
Inverse Functions
654
4
Natural Logarithms and the Number e
658
15
Continuous Growth and the Number e
659
5
Solving Exponential Equations
664
3
Charging a Capacitor and the Number e
667
1
The Slope Function for Exponential and Logarithmic Functions
668
5
Using Logarithmic Scales
673
10
The Mathematics of the Logarithmic Scale
674
8
Semilog Graphing on the Graphing Calculator
682
1
Analysis of the Cooling Data
683
13
Exponential Regression
683
1
Slope Function of Data
684
1
Vertical Transformation of the Data
685
1
The Accuracy of the Model
686
5
Summary and Review
691
3
Test
694
2
Systems of Equations and Inequalities
696
66
Maximizing the Profit
698
1
Preliminary Analysis
698
2
Review: Equations in One Variable
700
9
Solving Equations Without a Calculator
701
1
When to Use the Calculator?
702
1
Solving Equations with a Calculator
703
6
Solving Two Equations in Two Variables
709
18
Solving Two Equations: The Addition Method
711
1
Solving Two Equations: The Graphical Method
712
1
Solving Two Equations: The Substitution Method
713
3
Questions About the Addition Method
716
2
Application: Kirchhoff's Laws of Circuit Analysis
718
3
How Many Solutions Are Possible?
721
6
Inequalities in One Variable
727
13
Representing the Solution of an Inequality with a Graph
728
1
Solving an Inequality with Algebra
729
4
Solving an Inequality with a Calculator
733
2
Solving Inequalities: Binary Logic and the Step Function
735
3
Binary Logic and the Manufacturing Problem
738
2
Inequalities in Two Variables
740
12
The Graph of a System of Inequalities
740
5
Graphing Systems of Inequalities on the Calculator
745
1
Graphing the Systems for the Chapter Project
746
6
Linear Programming
752
10
What Is Linear Programming?
753
2
When the Maximum Occurs at an Unacceptable Point
755
1
Adding a New Constraint
756
3
Summary and Review
759
2
Test
761
1
Matrices and 3-D Graphing
762
88
Scaling and Rotating Points
764
1
Preliminary Analysis
764
2
Introduction to the Transformation of Points
766
14
Scaling
767
3
Rotation
770
2
Rotation and Scaling Together
772
2
The Trigonometry of Rotation
774
6
Introduction to Matrix Algebra
780
19
Matrix Multiplication
781
4
Matrix Algebra on the TI-83
785
1
Which Matrices Can Be Multiplied?
786
1
Choosing the Dimensions of a Matrix
787
2
Matrices and Transformation of Points in Two Dimensions
789
10
Matrices and Equation Solving
799
11
Representing Systems with Matrices
799
2
Solving a Matrix Equation
801
9
Graphing in Three Dimensions
810
7
Cartesian Coordinates in Three Dimensions
810
1
Computing Distances in Space
811
4
Motion in 3-D
815
2
Plotting Equations in 3-D
817
10
Solving Systems in Three or More Dimensions
822
5
Curves and Surfaces in 3-D
827
10
Parametric Equations in 3-D
827
3
Cylindrical Coordinates
830
2
Spherical Coordinates
832
5
Rotations and Translations in Three Dimensions
837
13
Scaling in Three Dimensions
838
1
Rotation in Three Dimensions
838
3
Summary and Review
841
7
Test
848
2
Modeling with Probability and Statistics
850
65
Assessing Quality on the Assembly Line
852
1
Preliminary Analysis
852
4
Looking at Data
856
11
Data Analysis---Failure Rate
857
2
Data Analysis---Throwing Two Dice
859
2
Analyzing Data with the TI-83
861
1
Representing Data Graphically---The Histogram
862
5
Using Probability to Model Uncertainty
867
13
Translating English to Mathematics
869
1
How Many Ways Can It Happen---Adding Probabilities
870
2
Expected Number: How Well Can We Predict?
872
8
Probability of Binary Events
880
12
Independent Events---Multiplying Probabilities
880
3
Summary of Probability So Far
883
4
Counting Events
887
5
Analyzing Games of Chance
892
13
Card Games
892
1
Dice Games, Odds, and Expected Return
893
5
Roulette
898
2
State Lotteries
900
5
Solving the Chapter Project
905
10
Summary and Review
909
4
Test
913
2
Solutions to Selected Exercises
915
84
Index of Applications
999
2
Index
1001