Calculus : A Complete Course

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

• ISBN13: 9780201441406
• ISBN10: 0201441403
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Addison Wesley

Summary

Written by an experienced author team with expertise in the use of technology and NCTM guidelines, this text provides an emphasis on multiple representations of concepts and an abundance of worked examples. Calculus is explored through the interpretation of graphs and tables as well as through the application of analytical methods. Rich exercises include graphical and data-based problems, and interesting real-life applications in biology, business, chemistry, economics, engineering, finance, physics, the social sciences and statistics. Stepped Explorations throughout the text provide guided investigations of key concepts and help students build problem-solving skills. A grapher is required.

Table of Contents

Supplements	vii
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	(16)
Key Terms	569	(1)
Review Exercises	569	(6)
Vectors and Analytic Geometry in Space
Cartesian (Rectangular) Coordinates and Vectors in Space	575	(11)
Dot Products	586	(7)
Cross Products	593	(7)
Lines and Planes in Space	600	(7)
Cylinders and Cylindrical Coordinates	607	(7)
Quadric Surfaces	614	(17)
Key Terms	625	(1)
Review Exercises	626	(5)
Vector-Valued Functions and Motion in Space
Vector-Valued Functions and Space Curves	631	(14)
Arc Length and the Unit Tangent Vector T	645	(4)
Curvature, Torsion, and the TNB Frame	649	(12)
Planetary Motion and Satellites	661	(14)
Key Terms	670	(1)
Review Exercises	671	(4)
Multivariable Functions and Their Derivatives
Functions of Several Variables	675	(11)
Limits and Continuity in Higher Dimensions	686	(7)
Partial Derivatives	693	(10)
Differentiability, Linearization, and Differentials	703	(11)
The Chain Rule	714	(9)
Directional Derivatives, Gradient Vectors, and Tangent Planes	723	(13)
Extreme Values and Saddle Points	736	(10)
Lagrange Multipliers	746	(15)
Key Terms	756	(1)
Review Exercises	756	(5)
Multiple Integrals
Double Integrals	761	(12)
Areas, Moments, and Centers of Mass	773	(11)
Double Integrals in Polar Form	784	(6)
Triple Integrals in Rectangular Coordinates	790	(9)
Masses and Moments in Three Dimensions	799	(6)
Triple Integrals in Cylindrical and Spherical Coordinates	805	(11)
Substitutions in Multiple Integrals	816	(13)
Key Terms	825	(1)
Review Exercises	825	(4)
Integration in Vector Fields
Line Integrals	829	(6)
Vector Fields, Work, Circulation, and Flux	835	(10)
Path Independence, Potential Functions, and Conservative Fields	845	(10)
Green's Theorem in the Plane	855	(11)
Surface Area and Surface Integrals	866	(12)
Parametrized Surfaces	878	(8)
Stokes's Theorem	886	(10)
The Divergence Theorem and a Unified Theory	896	(16)
Key Terms	908	(1)
Review Exercises	908	(4)
Cumulative Review Exercises
(Chapters 1--10)	912	(4)
(Chapters 11--15)	916	(5)
Appendices
A1 Formulas from Precalculus Mathematics	921	(4)
A2 Mathematical Induction	925	(3)
A3 Using the Limit Definition	928	(8)
A4 Proof of the Chain Rule	936	(1)
A5 Conic Sections	937	(32)
A6 Hyperbolic Functions	969	(10)
A7 A Brief Table of Integrals	979	(6)
A8 Determinants and Cramer's Rule	985	(10)
Glossary	995	(20)
Selected Answers	1015	(124)
Applications Index	1139	(6)
Index	1145