Calculus

by Gerald Bradley; Karl J. Smith

• ISBN13: 9780136601357
• ISBN10: 0136601359
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Prentice Hall

Summary

Built from the ground up to meet the needs of today's calculus learners, "Calculus" was the first book to pair a complete calculus syllabus with the best elements of reform like extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking book has been crafted and honed, making it "the" book 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

Forward	xii
Preface	xv
Functions and Graphs	1	(72)
Preliminaries	2	(13)
Lines in the Plane	15	(9)
Functions	24	(10)
Graphs of Functions	34	(10)
Inverse Functions; Inverse Trigonometric Functions	44	(10)
Exponential and Logarithmic Functions	54	(19)
Chapter 1 Review	68	(5)
Limits and Continuity	73	(54)
What Is Calculus?	74	(11)
The Limit of a Function	85	(12)
Properties of Limits	97	(10)
Continuity	107	(20)
Chapter 2 Review	117	(5)
Guest Essay: ``Calculus Was Inevitable,''	122	(5)
John Troutman
Differentiation	127	(88)
An Introduction to the Derivative: Tangents	128	(15)
Techniques of Differentiation	143	(9)
Derivatives of Trigonometric, Exponential, and Logarithmic Functions	152	(7)
Rates of Change: Rectilinear Motion	159	(10)
The Chain Rule	169	(8)
Implicit Differentiation	177	(12)
Related Rates and Applications	189	(8)
Linear Approximation and Differentials	197	(18)
Chapter 3 Review	209	(4)
Group Research Project: Chaos	213	(2)
Additional Applications of the Derivative	215	(102)
Extreme Values of a Continuous Function	216	(12)
The Mean Value Theorem	228	(7)
First-Derivative Test	235	(11)
Concavity and the Second-Derivative Test	246	(13)
Curve Sketching: Limits Involving Infinity and Asymptotes	259	(13)
Optimization in the Physical Sciences and Engineering	272	(14)
Optimization in Business, Economics, and the Life Sciences	286	(14)
I'Hopital's Rule	300	(17)
Chapter 4 Review	309	(6)
Group Research Project: Wine Barrel Capacity	315	(2)
Integration	317	(88)
Antidifferentiation	318	(11)
Area as the Limit of a Sum	329	(8)
Riemann Sums and the Definite Integral	337	(13)
The Fundamental Theorems of Calculus	350	(7)
Integration by Substitution	357	(7)
Introduction to Differential Equations	364	(13)
The Mean Value Theorem for Integrals; Average Value	377	(6)
Numerical Integration: The Trapezoidal Rule and Simpson's Rule	383	(8)
An Alternative Approach: The Logarithm as an Integral	391	(14)
Chapter 5 Review	396	(5)
Guest Essay: ``Kinematics of Jogging,''	401	(4)
Ralph Boas
Additional Applications of the Integral	405	(60)
Area Between Two Curves	406	(9)
Volume by Disks and Washers	415	(11)
Volume by Shells	426	(7)
Arc Length and Surface Area	433	(8)
Physical Applications: Work, Liquid Force, and Centroids	441	(24)
Chapter 6 Review	454	(6)
Group Research Project: Houdini's Escape	460	(1)
Cumulative Review Problems for Chapters 1--6	461	(4)
Methods of Integration	465	(74)
Review of Substitution and Integration by Table	466	(9)
Integration by Parts	475	(6)
Trigonometric Methods	481	(7)
The Method of Partial Fractions	488	(11)
Summary of Integration Techniques	499	(4)
First-Order Differential Equations	503	(12)
Improper Integrals	515	(10)
The Hyperbolic and Inverse Hyperbolic Functions	525	(14)
Chapter 7 Review	533	(5)
Group Research Project: Buoy Design	538	(1)
Infinite Series	539	(86)
Sequences and Their Limits	540	(12)
Introduction to Infinite Series: Geometric Series	552	(9)
The Integral Test: p-Series	561	(8)
Comparison Tests	569	(6)
The Ratio Test and the Root Test	575	(7)
Alternating Series; Absolute and Conditional Convergence	582	(10)
Power Series	592	(10)
Taylor and Maclaurin Series	602	(23)
Chapter 8 Review	619	(4)
Group Research Project: Elastic Tightrope Project	623	(2)
Polar Coordinates and Parametric Forms	625	(42)
The Polar Coordinate System	626	(5)
Graphing in Polar Coordinates	631	(10)
Area and Tangent Lines in Polar Coordinates	641	(10)
Parametric Representation of Curves	651	(16)
Chapter 9 Review	661	(3)
Group Research Project: Security Systems	664	(3)
Vectors in the Plane and in Space	667	(60)
Vectors in the Plane	668	(8)
Quadric Surfaces and Graphing in Three Dimensions	676	(10)
The Dot Product	686	(10)
The Cross Product	696	(9)
Lines and Planes in Space	705	(11)
Vector Methods for Measuring Distance in R3	716	(11)
Chapter 10 Review	721	(5)
Group Research Project: Star Trek	726	(1)
Vector Valued Functions	727	(62)
Introduction to Vector Functions	728	(8)
Differentiation and Integration of Vector Functions	736	(11)
Modeling Ballistics and Planetary Motion	747	(10)
Unit Tangent and Normal Vectors; Curvature	757	(13)
Tangential and Normal Components of Acceleration	770	(19)
Chapter 11 Review	777	(4)
Guest Essay: ``The Stimulation of Science,''	781	(5)
Howard Eves
Cumulative Review Problems for Chapters 7--11	786	(3)
Partial Differentiation	789	(90)
Functions of Several Variables	790	(10)
Limits and Continuity	800	(7)
Partial Derivatives	807	(10)
Tangent Planes, Approximations, and Differentiability	817	(10)
Chain Rules	827	(8)
Directional Derivatives and the Gradient	835	(13)
Extrema of Functions of Two Variables	848	(13)
Lagrange Multipliers	861	(18)
Chapter 12 Review	871	(6)
Group Research Project': Desertification	877	(2)
Multiple Integration	879	(78)
Double Integration over Rectangular Regions	880	(9)
Double Integration over Non-Rectangular Regions	889	(8)
Double Integration in Polar Coordinates	897	(9)
Surface Area	906	(8)
Triple Integrals	914	(10)
Mass, Moments, and Probability Density Functions	924	(11)
Cylindrical and Spherical Coordinates	935	(9)
Jacobians: Change of Variables	944	(13)
Chapter 13 Review	950	(6)
Group Research Project: Space-Capsule Design	956	(1)
Vector Analysis	957	(72)
Properties of a Vector Field: Divergence and Curl	958	(8)
Line Integrals	966	(10)
Independence of Path	976	(9)
Green's Theorem	985	(10)
Surface Integration	995	(7)
Stokes' Theorem	1002	(8)
Divergence Theorem	1010	(19)
Chapter 14 Review	1019	(5)
Guest Essay: ``Continuous vs. Discrete Mathematics,''	1024	(5)
William F. Lucas
Introduction to Differential Equations	1029
First-Order Differential Equations	1030
Second-Order Homogeneous Linear Differential Equations	1041
Second-Order Nonhomogeneous Linear Differential Equations	1052
Chapter 15 Review	1062
Group Research Project: Save the Perch Project	1066
Cumulative Review Problems for Chapters 12--15	1068
APPENDICES
A. Introduction to the Theory of limits	A-1
B. Selected Proofs	A-9
C. Significant Digits	A-20
D. Short Table of Integrals	A-24
E. Answers to Selected Problems	A-33
F. Credits	A-74
Index	A-77