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Multivariable Calculus,9780534359485
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Multivariable Calculus

by
Edition:
4th
ISBN13:

9780534359485

ISBN10:
0534359485
Format:
Paperback
Pub. Date:
6/4/1999
Publisher(s):
Brooks Cole
List Price: $96.00
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Summary

These best-selling texts differ from CALCULUS, FOURTH EDITION in that the exponential and logarithmic functions are covered earlier. In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

Table of Contents

Key Definitions, Properties, and Theorems xvii
11 Parametric Equations and Polar Coordinates
674(52)
11.1 Curves Defined by Parametric Equations
675(7)
Laboratory Project Families of Hypocycloids
682(1)
11.2 Tangents and Areas
682(7)
Laboratory Project Bezier Curves
689(1)
11.3 Arc Length and Surface Area
689(5)
11.4 Polar Coordinates
694(10)
11.5 Areas and Lengths in Polar Coordinates
704(5)
11.6 Conic Sections
709(7)
11.7 Conic Sections in Polar Coordinates
716(6)
Review
722(2)
Problems Plus
724(2)
12 Infinite Sequences and Series
726(90)
12.1 Sequences
727(11)
Laboratory Project Logistic Sequences
738(1)
12.2 Series
738(10)
12.3 The Integral Test and Estimates of Sums
748(7)
12.4 The Comparison Tests
755(5)
12.5 Alternating Series
760(5)
12.6 Absolute Convergence and the Ratio and Root Tests
765(7)
12.7 Strategy for Testing Series
772(2)
12.8 Power Series
774(5)
12.9 Representations of Functions as Power Series
779(6)
12.10 Taylor and Maclaurin Series
785(11)
12.11 The Binomial Series
796(4)
Writing Project How Newton Discovered the Binomial Series
799(1)
12.12 Applications of Taylor Polynomials
800(9)
Applied Project Radiation from the Stars
808(1)
Review
809(3)
Problems Plus
812(4)
13 Vectors and the Geometry of Space
816(54)
13.1 Three-Dimensional Coordinate Systems
817(5)
13.2 Vectors
822(8)
13.3 The Dot Product
830(7)
13.4 The Cross Product
837(9)
Discovery Project The Geometry of a Tetrahedron
845(1)
13.5 Equations of Lines and Planes
846(9)
13.6 Cylinders and Quadric Surfaces
855(6)
13.7 Cylindrical and Spherical Coordinates
861(5)
Laboratory Project Families of Surfaces
866(1)
Review
866(3)
Problems Plus
869(1)
14 Vector Functions
870(36)
14.1 Vector Functions and Space Curves
871(6)
14.2 Derivatives and Integrals of Vector Functions
877(6)
14.3 Arc Length and Curvature
883(8)
14.4 Motion in Space: Velocity and Acceleration
891(10)
Applied Project Kepler's Laws
900(1)
Review
901(3)
Problems Plus
904(2)
15 Partial Derivatives
906(94)
15.1 Functions of Several Variables
907(14)
15.2 Limits and Continuity
921(8)
15.3 Partial Derivatives
929(13)
15.4 Tangent Planes and Linear Approximations
942(9)
15.5 The Chain Rule
951(9)
15.6 Directional Derivatives and the Gradient Vector
960(13)
15.7 Maximum and Minimum Values
973(12)
Applied Project Designing a Dumpster
983(1)
Discovery Project Quadratic Approximations and Critical Points
984(1)
15.8 Lagrange Multipliers
985(9)
Applied Project Rocket Science
992(1)
Applied Project Hydro-Turbine Optimization
993(1)
Review
994(4)
Problems Plus
998(2)
16 Multiple Integrals
1000(74)
16.1 Double Integrals over Rectangles
1001(9)
16.2 Iterated Integrals
1010(5)
16.3 Double Integrals over General Regions
1015(8)
16.4 Double Integrals in Polar Coordinates
1023(6)
16.5 Applications of Double Integrals
1029(10)
16.6 Surface Area
1039(3)
16.7 Triple Integrals
1042(10)
Discovery Project Volumes of Hyperspheres
1052(1)
16.8 Triple Integrals in Cylindrical and Spherical Coordinates
1052(8)
Applied Project Roller Derby
1058(1)
Discovery Project The Intersection of Three Cylinders
1059(1)
16.9 Change of Variables in Multiple Integrals
1060(8)
Review
1068(4)
Problems Plus
1072(2)
17 Vector Calculus
1074(84)
17.1 Vector Fields
1075(6)
17.2 Line Integrals
1081(12)
17.3 The Fundamental Theorem for Line Integrals
1093(9)
17.4 Green's Theorem
1102(7)
17.5 Curl and Divergence
1109(8)
17.6 Parametric Surfaces and Their Areas
1117(10)
17.7 Surface Integrals
1127(12)
17.8 Stokes' Theorem
1139(6)
Writing Project Three Men and Two Theorems
1144(1)
17.9 The Divergence Theorem
1145(7)
17.10 Summary
1152(1)
Review
1153(3)
Problems Plus
1156(2)
18 Second-Order Differential Equations
1158
18.1 Second-Order Linear Equations
1159(6)
18.2 Nonhomogeneous Linear Equations
1165(7)
18.3 Applications of Second-Order Differential Equations
1172(8)
18.4 Series Solutions
1180(4)
Review
1184
Appendixes A1(38)
F Proofs of Theorems A2(3)
G Complex Numbers A5(8)
H Answers to Odd-Numbered Exercises A13(26)
Index A39


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