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Tables of Contents for Brief Calculus
Chapter/Section Title
Page #
Page Count
1 MEASURING CHANGE
1
84
1.1 HOW DO WE MEASURE CHANGE?
2
7
1.2 WHAT'S A FUNCTION?
9
13
1.3 LINEAR FUNCTIONS
22
13
1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS
35
12
1.5 EXPONENTIAL FUNCTIONS
47
15
1.6 POWER FUNCTIONS
62
9
1.7 FITTING FORMULAS TO DATA
71
8
REVIEW PROBLEMS
79
6
2 RATE OF CHANGE: THE DERIVATIVE
85
56
2.1 INSTANTANEOUS RATE OF CHANGE
86
8
2.2 THE DERIVATIVE
94
8
2.3 THE DERIVATIVE FUNCTION
102
8
2.4 INTERPRETATIONS OF THE DERIVATIVE
110
8
2.5 THE SECOND DERIVATIVE
118
6
2.6 MARGINAL COST AND REVENUE
124
10
REVIEW PROBLEMS
134
7
3 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL
141
56
3.1 ACCUMULATED CHANGE
142
9
3.2 THE DEFINITE INTEGRAL
151
11
3.3 THE DEFINITE INTEGRAL AS AREA
162
8
3.4 THE DEFINITE INTEGRAL AS AVERAGE VALUE
170
6
3.5 INTERPRETATIONS OF THE DEFINITE INTEGRAL
176
11
3.6 THE FUNDAMENTAL THEOREM OF CALCULUS
187
6
REVIEW PROBLEMS
193
4
4 A LIBRARY OF FUNCTIONS
197
68
4.1 THE NUMBER e
198
8
4.2 THE NATURAL LOGARITHM
206
10
4.3 NEW FUNCTIONS FROM OLD; POLYNOMIALS
216
11
4.4 PERIODIC FUNCTIONS
227
7
4.5 THE LOGISTIC CURVE
234
14
4.6 THE SURGE FUNCTION
248
9
REVIEW PROBLEMS
257
8
5 SHORT-CUTS TO DIFFERENTIATION
265
48
5.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
266
11
5.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
277
6
5.3 THE CHAIN RULE
283
5
5.4 THE PRODUCT RULE
288
4
5.5 DERIVATIVES OF PERIODIC FUNCTIONS
292
4
5.6 VERIFYING THE DERIVATIVE FORMULAS
296
6
5.7 FINDING ANTIDERIVATIVES
302
7
REVIEW PROBLEMS
309
4
6 APPLICATIONS
313
58
6.1 CRITICAL POINTS AND INFLECTION POINTS
314
13
6.2 OPTIMIZATION
327
9
6.3 MORE OPTIMIZATION: AVERAGE COST
336
8
6.4 APPLICATIONS OF THE DEFINITE INTEGRAL
344
12
6.5 CONSUMER AND PRODUCER SURPLUS
356
6
REVIEW PROBLEMS
362
9
7 FUNCTIONS OF MANY VARIABLES
371
66
7.1 UNDERSTANDING FUNCTIONS OF MANY VARIABLES
372
9
7.2 CONTOUR DIAGRAMS
381
18
7.3 THE PARTIAL DERIVATIVE
399
10
7.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
409
8
7.5 CRITICAL POINTS AND OPTIMIZATION
417
6
7.6 LAGRANGE MULTIPLIERS
423
8
REVIEW PROBLEMS
431
6
APPENDIX
437
 
A ROOTS AND ACCURACY
438
8
B COMPOUND INTEREST
446