Calculus,9780130631312

Calculus

by ; ; ;
Edition: 3rd
ISBN13: 9780130631312
ISBN10: 0130631310
Format: Hardcover
Pub. Date: 2002-01-01
Publisher(s): PRENTICE HALL SCHOOL GROUP
List Price: $149.58

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Table of Contents

Supplements xv
To the Student xvi
Prerequisites for Calculus
Lines
1(8)
Functions and Graphs
9(11)
Exponential Functions
20(6)
Parametric Equations
26(6)
Functions and Logarithms
32(9)
Trigonometric Functions
41(14)
Key Terms
51(1)
Review Exercises
52(3)
Limits and Continuity
Rates of Change and Limits
55(10)
Limits Involving Infinity
65(8)
Continuity
73(9)
Rates of Change and Tangent Lines
82(13)
Key Terms
90(1)
Review Exercises
91(4)
Derivatives
Derivative of a Function
95(10)
Differentiability
105(7)
Rules for Differentiation
112(10)
Velocity and Other Rates of Change
122(12)
Derivatives of Trigonometric Functions
134(7)
Chain Rule
141(8)
Implicit Differentiation
149(8)
Derivatives of Inverse Trigonometric Functions
157(6)
Derivatives of Exponential and Logarithmic Functions
163(14)
Calculus at Work
171(1)
Key Terms
172(1)
Review Exercises
172(5)
Applications of Derivatives
Extreme Values of Functions
177(9)
Mean Value Theorem
186(8)
Connecting f' and f'' with the Graph of f
194(12)
Modeling and Optimization
206(14)
Linearization and Newton's Method
220(12)
Related Rates
232(15)
Key Terms
241(1)
Review Exercises
242(5)
The Definite Integral
Estimating with Finite Sums
247(11)
Definite Integrals
258(10)
Definite Integrals and Antiderivatives
268(9)
Fundamental Theorem of Calculus
277(12)
Trapezoidal Rule
289(14)
Key Terms
297(1)
Review Exercises
298(3)
Calculus at Work
301(2)
Differential Equations and Mathematical Modeling
Antiderivatives and Slope Fields
303(12)
Integration by Substitution
315(8)
Integration by Parts
323(7)
Exponential Growth and Decay
330(12)
Population Growth
342(8)
Numerical Methods
350(13)
Calculus at Work
357(1)
Key Terms
357(1)
Review Exercises
358(5)
Applications of Definite Integrals
Integral as Net Change
363(11)
Areas in the Plane
374(9)
Volumes
383(12)
Lengths of Curves
395(6)
Applications from Science and Statistics
401(16)
Calculus at Work
412(1)
Key Terms
412(1)
Review Exercises
413(4)
L'Hopital's Rule, Improper Integrals, and Partial Fractions
L'Hopital's Rule
417(8)
Relative Rates of Growth
425(8)
Improper Integrals
433(11)
Partial Fractions and Integral Tables
444(13)
Key Terms
453(1)
Review Exercises
454(3)
Infinite Series
Power Series
457(12)
Taylor Series
469(11)
Taylor's Theorem
480(7)
Radius of Convergence
487(9)
Testing Convergence at Endpoints
496(17)
Key Terms
508(1)
Review Exercises
509(2)
Calculus at Work
511(2)
Parametric, Vector, and Polar Functions
Parametric Functions
513(7)
Vectors in the Plane
520(9)
Vector-valued Functions
529(10)
Modeling Projectile Motion
539(13)
Polar Coordinates and Polar Graphs
552(7)
Calculus of Polar Curves
559(14)
Key Terms
569(1)
Review Exercises
569(4)
Cumulative Review Exercises 573(62)
Appendices
A1 Formulas from Precalculus Mathematics
577(4)
A2 Mathematical Induction
581(3)
A3 Using the Limit Definition
584(8)
A4 Proof of the Chain Rule
592(1)
A5 Conic Sections
593(25)
A6 Hyperbolic Functions
618(10)
A7 A Brief Table of Integrals
628(7)
Glossary 635(12)
Selected Answers/Solutions 647(124)
Applications Index 771(6)
Index 777

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