Calculus

by Finney, Ross L.; Demana, Franklin; Waits, Bert K.; Kennedy, Daniel

• ISBN13: 9780130631312
• ISBN10: 0130631310
• Edition: 3rd
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: PRENTICE HALL SCHOOL GROUP

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