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Calculus : Concepts and Contexts, Single Variable

ISBN: 9780534344504 | 053434450X
Edition: 1st
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 7/17/1997

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Table of Contents
A PREVIEW OF CALCULUS2(8)
1 FUNCTIONS AND MODELS
10(84)
1.1 Four Ways to Represent a Function
12(14)
... MORE
1.2 New Functions from Old Functions
26(15)
1.3 Graphing Calculators and Computers
41(7)
1.4 Parametric Curves
48(8)
Laboratory Project: Families of Hypocycloids
55(1)
1.5 Exponential Functions
56(7)
1.6 Inverse Functions and Logarithms
63(12)
1.7 Models and Curve Fitting
75(9)
Review
84(3)
Principles of Problem Solving
87(7)
2 LIMITS AND DERIVATIVES
94(96)
2.1 The Tangent and Velocity Problems
96(5)
2.2 The Limit of a Function
101(10)
2.3 Calculating Limits Using the Limit Laws
111(9)
2.4 Continuity
120(10)
2.5 Limits Involving Infinity
130(12)
2.6 Tangents, Velocities, and Other Rates of Change
142(9)
2.7 Derivatives
151(7)
Writing Project: Early Methods for Finding Tangents
157(1)
2.8 The Derivative as a Function
158(13)
2.9 Linear Approximations
171(4)
2.10 What Does f' Say about f?
175(7)
Review
182(4)
Focus on Problem Solving
186(4)
3 DIFFERENTIATION RULES
190(76)
3.1 Derivatives of Polynomials and Exponential Functions
192(9)
3.2 The Product and Quotient Rules
201(6)
3.3 Rates of Change in the Natural and Social Sciences
207(13)
3.4 Derivatives of Trigonometric Functions
220(7)
3.5 The Chain Rule
227(12)
Laboratory Project: Bezier Curves
237(1)
Applied Project: Where Should a Pilot Start Descent?
238(1)
3.6 Implicit Differentiation
239(8)
3.7 Derivatives of Logarithmic Functions
247(7)
Discovery Project: Hyperbolic Functions
253(1)
3.8 Linear Approximations and Differentials
254(6)
Laboratory Project: Taylor Polynomials
259(1)
Review
260(3)
Focus on Problem Solving
263(3)
4 APPLICATIONS OF DIFFERENTIATION
266(82)
4.1 Related Rates
268(6)
4.2 Maximum and Minimum Values
274(9)
Applied Project: The Calculus of Rainbows
282(1)
4.3 Derivatives and the Shapes of Curves
283(11)
4.4 Graphing with Calculus and Calculators
294(7)
4.5 Indeterminate Forms and L'Hospital's Rule
301(9)
Writing Project: The Origins of L'Hospital's Rule
310(1)
4.6 Optimization Problems
310(12)
Applied Project: The Shape of a Can
321(1)
4.7 Applications to Economics
322(5)
4.8 Newton's Method
327(5)
4.9 Antiderivatives
332(8)
Review
340(4)
Focus on Problem Solving
344(4)
5 INTEGRALS
348(98)
5.1 Areas and Distances
350(11)
5.2 The Definite Integral
361(11)
5.3 Evaluating Definite Integrals
372(11)
Discovery Project: Area Functions
382(1)
5.4 The Fundamental Theorem of Calculus
383(10)
Writing Project: Newton, Leibniz, and the Invention of Calculus
392(1)
5.5 The Substitution Rule
393(9)
5.6 Integration by Parts
402(6)
5.7 Integration Using Tables and Computer Algebra Systems
408(8)
Discovery Project: Patterns in Integrals
414(2)
5.8 Approximate Integration
416(11)
5.9 Improper Integrals
427(10)
Review
437(5)
Focus on Problem Solving
442(4)
6 APPLICATIONS OF INTEGRATION
446(56)
6.1 More about Areas
448(7)
6.2 Volumes
455(9)
6.3 Arc Length
464(5)
6.4 Average Value of a Function
469(4)
Applied Project: Where to Sit at the Movies
472(1)
6.5 Applications to Physics and Engineering
473(11)
6.6 Applications to Economics and Biology
484(5)
6.7 Probability
489(7)
Review
496(3)
Focus on Problem Solving
499(3)
7 DIFFERENTIAL EQUATIONS
502(56)
7.1 Modeling with Differential Equations
504(5)
7.2 Direction Fields
509(5)
7.3 Euler's Method
514(4)
7.4 Separable Equations
518(9)
Applied Project: Which is Faster, Going Up or Coming Down?
526(1)
7.5 Exponential Growth and Decay
527(10)
Applied Project: Calculus and Baseball
536(1)
7.6 The Logistic Equation
537(9)
7.7 Predator-Prey Systems
546(7)
Review
553(3)
Focus on Problem Solving
556(2)
8 INFINITE SEQUENCES AND SERIES
558
8.1 Sequences
560(10)
Laboratory Project: Logistic Sequences
569(1)
8.2 Series
570(9)
8.3 The Integral and Comparison Tests; Estimating Sums
579(10)
8.4 Other Convergence Tests
589(8)
8.5 Power Series
597(6)
8.6 Representations of Functions as Power Series
603(5)
8.7 Taylor and Maclaurin Series
608(11)
8.8 The Binomial Series
619(5)
Writing Project: How Newton Discovered the Binomial Series
623(1)
8.9 Applications of Taylor Polynomials
624(9)
Applied Project: Radiation from the Stars
632(1)
8.10 Using Series to Solve Differential Equations
633(4)
Review
637(3)
Focus on Problem Solving
640
APPENDIXESA1(112)
A Intervals, Inequalities, and Absolute ValuesA2(5)
B Coordinate GeometryA7(12)
C TrigonometryA19(13)
D Precise Definitions of LimitsA32(8)
E A Few ProofsA40(2)
F Integration of Rational Functions by Partial FractionsA42(9)
G Polar CoordinatesA51(16)
H Complex NumbersA67(9)
I Answers to Odd-Numbered ExercisesA76(37)
INDEXA113

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