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Tables of Contents for Applied Calculus
Chapter/Section Title
Page #
Page Count
Functions and Change
1
92
What is a Function?
2
5
Linear Functions
7
6
Rates of Change
13
9
Applications of Functions to Economics
22
10
Exponential Functions
32
7
The Natural Logarithm
39
4
Exponential Growth and Decay
43
8
New Functions from Old
51
5
Proportionality, Power Functions, and Polynomials
56
7
Periodic Functions
63
30
Review Problems
69
5
Projects
74
1
Focus on Modeling
75
1
Fitting Formulas to Data
75
7
Compound Interest and the Number e
82
6
Focus on Theory
88
1
Limits to Infinity and End Behavior
88
5
Rate of Change: The Derivative
93
42
Instantaneous Rate of Change
94
7
The Derivative Function
101
5
Interpretations of the Derivative
106
7
The Second Derivative
113
4
Marginal Cost and Revenue
117
18
Review Problems
124
3
Projects
127
2
Focus on Theory
129
1
Limits, Continuity, and the Definition of the Derivative
129
6
Short-Cuts to Differentiation
135
30
Derivative Formulas for Powers and Polynomials
136
6
Exponential and Logarithmic Functions
142
5
The Chain Rule
147
3
The Product and Quotient Rules
150
3
Derivatives of Periodic Functions
153
12
Review Problems
157
2
Projects
159
1
Focus on Theory
160
1
Establishing the Derivative Formulas
160
3
Focus on Practice
163
1
Differentiation
163
2
Using the Derivative
165
54
Local Maxima and Minima
166
5
Inflection Points
171
5
Global Maxima and Minima
176
7
Profit, Cost, and Revenue
183
5
Average Cost
188
5
Elasticity of Demand
193
5
Logistic Growth
198
8
The Surge Function and Drug Concentration
206
13
Review Problems
213
4
Projects
217
2
Accumulated Change: The Definite Integral
219
36
Accumulated Change
220
5
The Definite Integral
225
7
The Definite Integrals as Area
232
5
Interpretations of the Definite Integral
237
6
The Fundamental Theorem of Calculus
243
12
Review Problems
246
4
Projects
250
2
Focus on Theory
252
1
Theorems About Definite Integrals
252
3
Using the Definite Integral
255
22
Average Value
256
3
Consumer and Producer Surplus
259
6
Present and Future Value
265
3
Relative Growth Rates
268
9
Review Problems
272
3
Projects
275
2
Antiderivatives
277
24
Constructing Antiderivatives Analytically
278
4
Integration by Substitution
282
4
Using the Fundamental Theorem to Find Definite Integrals
286
4
Analyzing Antiderivatives Graphically and Numerically
290
11
Review Problems
296
2
Projects
298
1
Focus on Practice
299
1
Integration
299
2
Probability
301
20
Density Functions
302
4
Cumulative Distribution Functions and Probability
306
6
The Median and the Mean
312
9
Review Problems
318
2
Projects
320
1
Functions of Several Variables
321
54
Understanding Functions of Two Variables
322
4
Contour Diagrams
326
11
Partial Derivatives
337
8
Computing Partial Derivatives Algebraically
345
7
Critical Points and Optimization
352
5
Constrained Optimization
357
18
Review Problems
365
3
Projects
368
1
Focus on Theory
369
1
Deriving the Formula for a Regression Line
369
6
Mathematical Modeling Using Differential Equations
375
44
Mathematical Modeling: Setting Up a Differential Equation
376
4
Solutions of Differential Equations
380
4
Slope Fields
384
6
Exponential Growth and Decay
390
5
Applications and Modeling
395
9
Modeling the Interaction of Two Populations
404
5
Modeling the Spread of a Disease
409
10
Review Problems
414
2
Projects
416
3
Geometric Series
419
18
Geometric Series
420
5
Applications to Business and Economics
425
3
Applications to Life Sciences
428
9
Review Problems
434
1
Projects
435
2
APPENDIX
437
10
Spreadsheet Projects
438
9
1. Malthus: Population Outstrips Food Supply
438
1
2. Credit Card Debt
439
1
3. Choosing a Bank Loan
440
1
4. Comparing Home Mortgages
441
1
5. Present Value of Lottery Winnings
442
1
6. Comparing Investments
442
1
7. Investing for the Future: Tuition Payments
443
1
8. Verhulst: The Logistic Model
443
1
9. The Spread of Information: A Comparison of Two Models
444
3
Answers to Odd-Numbered Problems
447
22
Index
469