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Calculus : Concepts and Contexts

by
Edition:
2nd
ISBN13:

9780534377182

ISBN10:
0534377181
Format:
Paperback
Pub. Date:
12/13/2000
Publisher(s):
Brooks Cole
List Price: $197.00

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Summary

James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

Table of Contents

A Preview of Calculus 2(8)
Functions and Models
10(84)
Four Ways to Represent a Function
11(13)
Mathematical Models
24(14)
New Functions from Old Functions
38(11)
Graphing Calculators and Computers
49(7)
Exponential Functions
56(8)
Inverse Functions and Logarithms
64(11)
Parametric Curves
75(19)
Laboratory Project Running Circles around Circles
83(1)
Review
84(4)
Priciples of Problem Solving
88(6)
Limits and Derivatives
94(94)
The Tangent and Velocity Problems
95(5)
The Limit of a Function
100(10)
Calculating Limits Using the Limit Laws
110(9)
Continuity
119(11)
Limits Involving Infinity
130(12)
Tangents, Velocities, and Other Rates of Change
142(8)
Derivatives
150(7)
Writing Project Early Methods for Finding Tangents
157(1)
The Derivative as a Function
157(14)
Linear Approximations
171(4)
What Does f' Say about f?
175(13)
Review
181(4)
Focus on Problem Solving
185(3)
Differentiation Rules
188(76)
Derivatives of Polynomials and Exponential Functions
189(10)
Applied Project Building a Better Roller Coaster
198(1)
The Product and Quotient Rules
199(7)
Rates of Change in the Natural and Social Sciences
206(12)
Derivatives of Trigonometric Functions
218(7)
The Chain Rule
225(12)
Laboratory Project Bezier Curves
236(1)
Applied Project Where Should a Pilot Start Descent?
237(1)
Implicit Differentiation
237(8)
Derivatives of Logarithmic Functions
245(7)
Discovery Project Hyperbolic Functions
251(1)
Linear Approximations and Differentials
252(12)
Laboratory Project Taylor Polynomials
257(1)
Review
258(3)
Focus on Problem Solving
261(3)
Applications of Differentiation
264(80)
Related Rates
265(6)
Maximum and Minimum Values
271(9)
Applied Project The Calculus of Rainbows
279(1)
Derivatives and the Shapes of Curves
280(11)
Graphing with Calculus and Calculators
291(7)
Indeterminate Forms and 1'Hospital's Rule
298(9)
Writing Project The Origins of l'Hospital's Rule
307(1)
Optimization Problems
307(12)
Applied Project The Shape of a Can
318(1)
Applications to Economics
319(5)
Newton's Method
324(5)
Antiderivatives
329(15)
Review
336(4)
Focus on Problem Solving
340(4)
Integrals
344(102)
Areas and Distances
345(12)
The Definite Integral
357(12)
Evaluating Definite Integrals
369(11)
Discovery Project Area Functions
379(1)
The Fundamental Theorem of Calculus
380(9)
Writing Project Newton, Leibniz, and the Invention of Calculus
388(1)
The Substitution Rule
389(7)
Integration by Parts
396(7)
Additional Techniques of Integration
403(6)
Integration Using Tables and Computer Algebra Systems
409(7)
Discovery Project Patterns in Integrals
415(1)
Approximate Integration
416(12)
Improper Integrals
428(18)
Review
438(4)
Focus on Problem Solving
442(4)
Applications of Integration
446(60)
More about Areas
447(6)
Volumes
453(14)
Discovery Project Rotating on a Slant
466(1)
Arc Length
467(6)
Discovery Project Arc Length Contest
472(1)
Average Value of a Function
473(3)
Applied Project Where to Sit at the Movies
476(1)
Applications to Physics and Engineering
476(11)
Applications to Economics and Biology
487(5)
Probability
492(14)
Review
499(3)
Focus on Problem Solving
502(4)
Differential Equations
506(56)
Modeling with Differential Equations
507(5)
Direction Fields and Euler's Method
512(10)
Separable Equations
522(9)
Applied Project Which Is Faster, Going Up or Coming Down?
530(1)
Exponential Growth and Decay
531(10)
Applied Project Calculus and Baseball
540(1)
The Logistic Equation
541(9)
Predator-Prey Systems
550(12)
Review
557(3)
Focus on Problem Solving
560(2)
Infinite Sequences and Series
562(84)
Sequences
563(10)
Laboratory Project Logistic Sequences
573(1)
Series
573(10)
The Integral and Comparison Tests; Estimating Sums
583(9)
Other Convergence Tests
592(8)
Power Series
600(5)
Representations of Functions as Power Series
605(6)
Taylor and Maclaurin Series
611(11)
The Binomial Series
622(4)
Writing Project How Newton Discovered the Binomial Series
626(1)
Applications of Taylor Polynomials
626(9)
Applied Project Radiation from the Stars
634(1)
Using Series to Solve Differential Equations
635(11)
Review
640(3)
Focus on Problem Solving
643(3)
Vectors and the Geometry of Space
646(58)
Three-Dimensional Coordinate Systems
647(5)
Vectors
652(9)
The Dot Product
661(6)
The Cross Product
667(9)
Discovery Project The Geometry of a Tetrahedron
675(1)
Equations of Lines and Planes
676(9)
Functions and Surfaces
685(9)
Cylindrical and Spherical Coordinates
694(10)
Laboratory Project Families of Surfaces
699(1)
Review
700(3)
Focus on Problem Solving
703(1)
Vector Functions
704(44)
Vector Functions and Space Curves
705(6)
Derivatives and Integrals of Vector Functions
711(6)
Arc Length and Curvature
717(8)
Motion in Space
725(11)
Applied Project Kepler's Laws
735(1)
Parametric Surfaces
736(12)
Review
742(3)
Focus on Problem Solving
745(3)
Partial Derivatives
748(90)
Functions of Several Variables
749(11)
Limits and Continuity
760(6)
Partial Derivatives
766(13)
Tangent Planes and Linear Approximations
779(11)
The Chain Rule
790(8)
Directional Derivatives and the Gradient Vector
798(13)
Maximum and Minimum Values
811(11)
Applied Project Designing a Dumpster
820(1)
Discovery Project Quadratic Approximations and Critical Points
821(1)
Lagrange Multipliers
822(16)
Applied Project Rocket Science
829(1)
Applied Project Hydro-Turbine Optimization
830(1)
Review
831(5)
Focus on Problem Solving
836(2)
Multiple Integrals
838(78)
Double Integrals over Rectangles
839(10)
Iterated Integrals
849(5)
Double Integrals over General Regions
854(9)
Double Integrals in Polar Coordinates
863(5)
Applications of Double Integrals
868(10)
Surface Area
878(5)
Triple Integrals
883(10)
Discovery Project Volumes of Hyperspheres
893(1)
Triple Integrals in Cylindrical and Spherical Coordinates
893(8)
Applied Project Roller Derby
900(1)
Discovery Project The Intersection of Three Cylinders
901(1)
Change of Variables in Multiple Integrals
901(15)
Review
910(4)
Focus on Problem Solving
914(2)
Vector Calculus
916
Vector Fields
917
Line Integrals
924
The Fundamental Theorem for Line Integrals
936
Green's Theorem
945
Curl and Divergence
952
Surface Integrals
960
Stokes' Theorem
971
Writing Project Three Men and Two Theorems
977
The Divergence Theorem
978
Summary
985
Review
986
Focus on Problem Solving
989
Appendixes A1
A Intervals, Inequalities, and Absolute Values
A2
B Coordinate Geometry
A7
C Trigonometry
A18
D Precise Definitions of Limits
A29
E A Few Proofs
A39
F Sigma Notation
A44
G Integration of Rational Functions by Partial Fractions
A50
H Polar Coordinates
A58
I Complex Numbers
A74
J Answers to Odd-Numbered Exercises
A83
Index A135


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