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Calculus

by
Edition:
4th
ISBN13:

9780534359492

ISBN10:
0534359493
Format:
Paperback
Pub. Date:
5/21/1999
Publisher(s):
Brooks Cole
List Price: $158.66

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Summary

Stewart's CALCULUS, FOURTH EDITION reflects the same old-world dedication to excellence that characterized the first three editions. It has been revised with dedication, precision, and patient care to further emphasize conceptual understanding. A phenomenon of the Stewart success is the texts' use in such a wide variety of colleges and universities throughout the world. Just as he teaches to every student in his classes from the most unprepared to the most mathematically gifted, Stewart writes to a range of students - adding the explanations that make ideas come alive as well as the problems that challenge. Stewart's heuristic examples reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject.

Table of Contents

A Preview of Calculus 2(8)
Functions and Models
10(56)
Four Ways to Represent a Function
11(13)
Mathematical Models
24(14)
New Functions from Old Functions
38(12)
Graphing Calculators and Computers
50(9)
Review
56(3)
Principles of Problem Solving
59(7)
Limits and Rates of Change
66(62)
The Tangent and Velocity Problems
67(5)
The Limit of a Function
72(12)
Calculating Limits Using the Limit Laws
84(10)
The Precise Definition of a Limit
94(10)
Continuity
104(10)
Tangents, Velocities, and Other Rates of Change
114(12)
Review
124(2)
Problems Plus
126(2)
Derivatives
128(94)
Derivatives
129(7)
Writing Project Early Methods for Finding Tangents
135(1)
The Derivative as a Function
136(11)
Differentiation Formulas
147(11)
Rates of Change in the Natural and Social Sciences
158(12)
Derivatives of Trigonometric Functions
170(7)
The Chain Rule
177(8)
Implicit Differentiation
185(7)
Higher Derivatives
192(7)
Applied Project *** Where Should a Pilot Start Descent?
199(1)
Related Rates
199(6)
Linear Approximations and Differentials
205(13)
Laboratory Project *** Taylor Polynomials
213(1)
Review
214(4)
Problems Plus
218(4)
Applications of Differentiation
222(90)
Maximum and Minimum Values
223(11)
Applied Project *** The Calculus of Rainbows
232(2)
The Mean Value Theorem
234(6)
How Derivatives Affect the Shape of a Graph
240(9)
Limits at Infinity; Horizontal Asymptotes
249(14)
Summary of Curve Sketching
263(8)
Graphing with Calculus and Calculators
271(6)
Optimization Problems
277(11)
Applied Project *** The Shape of a Can
287(1)
Applications to Economics
288(5)
Newton's Method
293(6)
Antiderivatives
299(11)
Review
306(4)
Problems Plus
310(2)
Integrals
312(58)
Areas and Distances
313(11)
The Definite Integral
324(13)
Discovery Project *** Area Functions
336(1)
The Fundamental Theorem of Calculus
337(9)
Indefinite Integrals and the Total Change Theorem
346(10)
Writing Project *** Newton, Leibniz, and the Invention of Calculus
355(1)
The Substitution Rule
356(11)
Review
363(4)
Problems Plus
367(3)
Applications of Integration
370(36)
Areas between Curves
371(7)
Volumes
378(11)
Volumes by Cylindrical Shells
389(5)
Work
394(4)
Average Value of a Function
398(5)
Review
401(2)
Problems Plus
403(3)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
406(96)
Inverse Functions
407(9)
Instructors may cover either Sections 7.2--7.4 or Sections 7.2*--7.4*. See the Preface.
Exponential Functions and Their Derivatives
416(12)
Logarithmic Functions
428(7)
Derivatives of Logarithmic Functions
435(10)
The Natural Logarithmic Function
445(8)
The Natural Exponential Function
453(7)
General Logarithmic and Exponential Functions
460(9)
Inverse Trigonometric Functions
469(9)
Applied Project *** Where to Sit at the Movies
478(1)
Hyperbolic Functions
478(7)
Indeterminate Forms and L'Hospital's Rule
485(15)
Writing Project *** The Origins of L'Hospital's Rule
496(1)
Review
496(4)
Problems Plus
500(2)
Techniques of Integration
502(72)
Integration by Parts
503(7)
Trigonometric Integrals
510(7)
Trigonometric Substitution
517(7)
Integration of Rational Functions by Partial Fractions
524(9)
Strategy for Integration
533(6)
Integration Using Tables and Computer Algebra Systems
539(7)
Discovery Project *** Patterns in Integrals
545(1)
Approximate Integration
546(11)
Improper Integrals
557(14)
Review
568(3)
Problems Plus
571(3)
Further Applications of Integration
574(40)
Arc Length
575(7)
Area of a Surface of Revolution
582(7)
Discovery Project *** Rotating on a Slant
588(1)
Applications to Physics and Engineering
589(9)
Applications to Economics and Biology
598(5)
Probability
603(9)
Review
610(2)
Problems Plus
612(2)
Differential Equations
614(60)
Modeling with Differential Equations
615(5)
Direction Fields and Euler's Method
620(9)
Separable Equations
629(8)
Applied Project *** Which Is Faster, Going Up or Coming Down?
636(1)
Exponential Growth and Decay
637(10)
Applied Project *** Calculus and Baseball
646(1)
The Logistic Equation
647(9)
Linear Equations
656(6)
Predator-Prey Systems
662(10)
Review
668(4)
Problems Plus
672(2)
Parametric Equations and Polar Coordinates
674(52)
Curves Defined by Parametric Equations
675(7)
Laboratory Project *** Families of Hypocycloids
682(1)
Tangents and Areas
682(7)
Laboratory Project *** Bezier Curves
689(1)
Arc Length and Surface Area
689(5)
Polar Coordinates
694(10)
Areas and Lengths in Polar Coordinates
704(5)
Conic Sections
709(7)
Conic Sections in Polar Coordinates
716(8)
Review
722(2)
Problems Plus
724(2)
Infinite Sequences and Series
726(90)
Sequences
727(11)
Laboratory Project *** Logistic Sequences
738(1)
Series
738(10)
The Integral Test and Estimates of Sums
748(7)
The Comparison Tests
755(5)
Alternating Series
760(5)
Absolute Convergence and the Ratio and Root Tests
765(7)
Strategy for Testing Series
772(2)
Power Series
774(5)
Representations of Functions as Power Series
779(6)
Taylor and Maclaurin Series
785(11)
The Binomial Series
796(4)
Writing Project *** How Newton Discovered the Binomial Series
799(1)
Applications of Taylor Polynomials
800(12)
Applied Project *** Radiation from the Stars
808(1)
Review
809(3)
Problems Plus
812(4)
Vectors and the Geometry of Space
816(54)
Three-Dimensional Coordinate Systems
817(5)
Vectors
822(8)
The Dot Product
830(7)
The Cross Product
837(9)
Discovery Project *** The Geometry of a Tetrahedron
845(1)
Equations of Lines and Planes
846(9)
Cylinders and Quadric Surfaces
855(6)
Cylindrical and Spherical Coordinates
861(8)
Laboratory Project *** Families of Surfaces
866(1)
Review
866(3)
Problems Plus
869(1)
Vector Functions
870(36)
Vector Functions and Space Curves
871(6)
Derivatives and Integrals of Vector Functions
877(6)
Arc Length and Curvature
883(8)
Motion in Space: Velocity and Acceleration
891(13)
Applied Project *** Kepler's Laws
900(1)
Review
901(3)
Problems Plus
904(2)
Partial Derivatives
906(94)
Functions of Several Variables
907(14)
Limits and Continuity
921(8)
Partial Derivatives
929(13)
Tangent Planes and Linear Approximations
942(9)
The Chain Rule
951(9)
Directional Derivatives and the Gradient Vector
960(13)
Maximum and Minimum Values
973(12)
Applied Project *** Designing a Dumpster
983(1)
Discovery Project *** Quadratic Approximations and Critical Points
984(1)
Lagrange Multipliers
985(13)
Applied Project *** Rocket Science
992(1)
Applied Project *** Hydro-Turbine Optimization
993(1)
Review
994(4)
Problems Plus
998(2)
Multiple Integrals
1000(74)
Double Integrals over Rectangles
1001(9)
Iterated Integrals
1010(5)
Double Integrals over General Regions
1015(8)
Double Integrals in Polar Coordinates
1023(6)
Applications of Double Integrals
1029(10)
Surface Area
1039(3)
Triple Integrals
1042(10)
Discovery Project *** Volumes of Hyperspheres
1052(1)
Triple Integrals in Cylindrical and Spherical Coordinates
1052(8)
Applied Project *** Roller Derby
1058(1)
Discovery Project *** The Intersection of Three Cylinders
1059(1)
Change of Variables in Multiple Integrals
1060(12)
Review
1068(4)
Problems Plus
1072(2)
Vector Calculus
1074(84)
Vector Fields
1075(6)
Line Integrals
1081(12)
The Fundamental Theorem for Line Integrals
1093(9)
Green's Theorem
1102(7)
Curl and Divergence
1109(8)
Parametric Surfaces and Their Areas
1117(10)
Surface Integrals
1127(12)
Stokes' Theorem
1139(6)
Writing Project *** Three Men and Two Theorems
1144(1)
The Divergence Theorem
1145(7)
Summary
1152(4)
Review
1153(3)
Problems Plus
1156(2)
Second-Order Differential Equations
1158(26)
Second-Order Linear Equations
1159(6)
Nonhomogeneous Linear Equations
1165(7)
Applications of Second-Order Differential Equations
1172(8)
Series Solutions
1180(4)
Review
1184
Appendixes 1(118)
A Intervals, Inequalities, and Absolute Values
2(8)
B Coordinate Geometry and Lines
10(6)
C Graphs of Second-Degree Equations
16(8)
D Trigonometry
24(10)
E Sigma Notation
34(5)
F Proofs of Theorems
39(9)
G Complex Numbers
48(8)
H Answers to Odd-Numbered Exercises
56(63)
Index 119


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