9780130918710

Calculus

by ; ;
  • ISBN13:

    9780130918710

  • ISBN10:

    0130918717

  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2002-01-01
  • Publisher: Pearson College Div

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

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Supplemental Materials

What is included with this book?

Summary

Built from the ground up to meet the needs of today's calculus learners,Calculuswas the first book to pair a complete calculus syllabus with the best elements of reformlike extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking book has been crafted and honed, making itthebook of choice for those seeking the best of both worlds.Numerous chapters offer an exciting choice of problem sets and include topics such as functions and graphs, limits and continuity, differentiation, additional applications of the derivative, integration, additional applications of the integral, methods of integration, infinite series, vectors in the plane and in space, vector-valued functions, partial differentiation, multiple integration, introduction to vector analysis, and introduction to differential equations.For individuals in fields related to engineering, science, or mathematics.

Table of Contents

Preface ix
Functions and Graphs
1(48)
Preliminaries
2(11)
Lines in the Plane
13(6)
Functions and Graphs
19(14)
Inverse Functions; Inverse Trigonometric Functions
33(16)
Chapter 1 Review
42(4)
Guest Essay: Calculus Was Inevitable, John Troutman
46(2)
Mathematical Essays
48(1)
Limits and Continuity
49(48)
The Limit of a Function
50(11)
Algebraic Computation of Limits
61(9)
Continuity
70(10)
Exponential and Logarithmic Functions
80(17)
Chapter 2 Review
92(5)
Differentiation
97(86)
An Introduction to the Derivative: Tangents
98(12)
Techniques of Differentiation
110(9)
Derivatives of Trigonometric, Exponential, and Logarithmic Functions
119(6)
Rates of Change: Modeling Rectilinear Motion
125(13)
The Chain Rule
138(8)
Implicit Differentiation
146(11)
Related Rates and Applications
157(8)
Linear Approximation and Differentials
165(18)
Chapter 3 Review
177(4)
Group Research Project: Chaos
181(2)
Additional Applications of the Derivative
183(88)
Extreme Values of a Continuous Function
184(11)
The Mean Value Theorem
195(6)
Using Derivatives to Sketch the Graph of a Function
201(16)
Curve Sketching with Asympototes: Limits Involving Infinity
217(12)
I'Hopital's Rule
229(9)
Optimization in the Physical Sciences and Engineering
238(12)
Optimization in Business, Economics, Economics, and the Life Sciences
250(21)
Chapter 4 Review
263(6)
Group Research Project: Wine Barrel Capacity
269(2)
Integration
271(84)
Antidifferentiation
272(10)
Area as the Limit of a Sum
282(8)
Riemann Sums and the Definite Integral
290(12)
The Fundamental Theorems of Calculus
302(7)
Integration by Substitution
309(7)
Introduction to Differential Equations
316(12)
The Mean Value Theorem for Integrals; Average Value
328(6)
Numerical Integration: The Trapezoidal Rule and Simpson's Rule
334(8)
An Alternative Approach: The Logarithm as an Integral
342(13)
Chapter 5 Review
346(5)
Guest Essay: Kinematics of Jogging, Ralph Boas
351(1)
Mathematical Essays
352(1)
Cumulative Review: Chapter 1--5
353(2)
Additional Applications of the Integral
355(70)
Area between two Curves
356(6)
Volume
362(13)
Polar Forms and Area
375(10)
Arc Length and Surface Area
385(10)
Physical Applications: Work, Liquid Force, and Centroids
395(12)
Applications to Business, Economics, and Life Sciences
407(18)
Chapter 6 Review
417(7)
Group Research Project: Houdini's Excape
424(1)
Methods of Integration
425(68)
Review of Substitution and Integration by Table
426(9)
Integration by Parts
435(6)
Trigonometric Methods
441(7)
Method of Partial Fractions
448(9)
Summary of Integration Techniques
457(4)
First-Order Differential Equations
461(11)
Improper Integrals
472(9)
Hyperbolic and Inverse Hyperbolic Functions
481(12)
Chapter 7 Review
487(4)
Group Research Project: Buoy Design
491(2)
Infinite Series
493(80)
Sequences and Their Limits
494(11)
Introduction to Infinite Series: Geometric Series
505(9)
The Integral Test; p-Series
514(7)
Comparison Tests
521(6)
The Ratio Test and the Root Test
527(6)
Alternating Series; Absolute and Conditional Convergence
533(11)
Power Series
544(9)
Taylor and Maclaurin Series
553(20)
Chapter 8 Review
566(4)
Group Research Project: Elastic Tightrope
570(1)
Cumulative Review: Chapters 6--8
571(2)
Vectors in the Plane and in Space
573(60)
Vectors in R2
574(8)
Coordinates and Vectors in R3
582(6)
The Dot Product
588(9)
The Cross Product
597(9)
Parametric Representation of Curves; Lines in R3
606(9)
Planes in R3
615(7)
Quadric Surfaces
622(11)
Chapter 9 Review
628(4)
Group Research Project: Star Trek
632(1)
Vector-Valued Functions
633(60)
Introduction to Vector Functions
634(8)
Differentiation and Integration of Vector Functions
642(9)
Modeling Ballistics and Planetary Motion
651(9)
Unit Tangent and Principal Unit Normal Vectors; Curvature
660(13)
Tangential and Normal Components of Acceleration
673(20)
Chapter 10 Review
679(5)
Guest Essay: The Stimulation of Science, Howard Eves
684(3)
Mathematical Essays
687(1)
Cumulative Review: Chapters 1--10
688(5)
Partial Differentiation
693(84)
Functions of Several Variables
694(7)
Limits and Continuity
701(9)
Partial Derivatives
710(10)
Tangent Planes, Approximations, and Differentiability
720(9)
Chain Rules
729(8)
Directional Derivatives and the Gradient
737(12)
Extrema of Functions of Two Variables
749(12)
Lagrange Multipliers
761(16)
Chapter 11 Review
770(5)
Group Research Project: Desertification
775(2)
Multiple Integration
777(82)
Double Integration over Rectangular Regions
778(9)
Double Integration over Nonrectangular Regions
787(8)
Double Integrals in Polar Coordinates
795(9)
Surface Area
804(8)
Triple Integrals
812(10)
Mass, Moments, and Probability Density Functions
822(11)
Cylindrical and Spherical Coordinates
833(10)
Jacobians: Change of Variables
843(16)
Chapter 12 Review
852(5)
Group Research Project: Space-Capsule Design
857(2)
Vector Analysis
859(76)
Properties of a Vector Field: Divergence and Curl
860(7)
Line Integrals
867(10)
The Fundamental Theorem and Path Independence
877(10)
Green's Theorem
887(11)
Surface Integrals
898(10)
Stokes' Theorem
908(8)
The Divergence Theorem
916(19)
Chapter 13 Review
924(5)
Guest Essay: Continuous vs. Discrete Mathematics
929(1)
Cumulative Review: Chapters 11--13
930(1)
Mathematical Essays
931(1)
Cumulative Review: Chapters 11--13
932(3)
Introduction to Differential Equations
935
First-Order Differential Equations
936
Second-Order Homogeneous Linear Differential Equations
947
Second-Order Nonhomogeneous Linear Differential Equations
957
Chapter 14 Review
966
Group Research Project: Save the Perch Project
969
Appendices
A Introduction to the Theory of Limits
A-1
B Selected Proofs
A-8
C Significant Digits
A-17
D Short Table of Integrals
A-21
E Trigonometric Formulas
A-31
F Answers to Selected Problems
A-34
G Credits
A-80
Index A-85

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