Calculus : A Complete Course,9780201441406

Calculus : A Complete Course

by ; ; ;
Edition: 2nd
ISBN13: 9780201441406
ISBN10: 0201441403
Format: Hardcover
Pub. Date: 2000-01-01
Publisher(s): Addison Wesley
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List Price: $221.20

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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

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