Table of contents for Multivariable calculus / James Stewart.


Bibliographic record and links to related information available from the Library of Congress catalog
Note: Electronic data is machine generated. May be incomplete or contain other coding.


Counter
Preface    xi
PARAMETRIC EQUATIONS AND POLAR COORDINATES                        656
1.1   Curves Defined by Parametric Equations  657
Laboratory  Project o Running  Circles Around  Circles  665
S1.2  Calculus with Parametric Curves  666
Laboratory Project  Bezier Curves  675
I .3  Polar Coordinates  675
S1.4  Areas and Lengths in Polar Coordinates  686
11.5  Conic Sections  690
S1.6  Conic Sections in Polar Coordinates  698
Review    705
Problems Plus  708
, INFINITE SEQUENCES AND SERIES              710
12.1  Sequences    711
Laboratory Project - Logistic Sequences  723
12.2  Series   723
12.3  The Integral Test and Estimates of Sums  733
12.4  The Comparison Tests   741
12.5  Alternating Series  746
12.6  Absolute Convergence and the Ratio and Root Tests  750
12.7  Strategy for Testing Series  757
12.8  Power Series   759
12.9  Representations of Functions as Power Series  764
12.10  Taylor and Maclaurin Series      770
Laboratory Project  An  Elusive  Limit  784
Writing Project H, ow Newton Discovered the Binomial Series  784
S12.1  Applications of Taylor Polynomials      785
Applied Project  Radiation  from  the Stars  793
Review     794
Probiems Plus   797
S13   VECTORS AND THE GEOMETRY OF SPACE                        800
13.1 Three-Dimensional Coordinate Systems         801
13.2   Vectors     806
13.3   The Dot Product      815
13.4   The Cross Product      822
Discovery Project , The Geometry of a Tetrahedron  830
13.5   Equations of Lines and Planes      830
Laboratory Project  Putting  3D  in  Perspective  840
53.6   Cylinders and Quadric Surfaces       840
Review     848
Problems Plus   85 i
14 J VECTOR FUNCTIONS                 852
14.1   Vector Functions and Space Curves       853
14.2   Derivatives and Integrals of Vector Functions     860
14.3   Arc Length and Curvature       866
14.4   Motion in Space: Velocity and Acceleration      874
Applied Project  Kepler's Laws  884
Review      885
Problems Pius   888
15 i PARTIAL DERIVATIVES               890
15. I  Functions of Several Variables      891
15.2   Limits and Continuity       906
15.3   Partial Derivatives     914
5.4   Tangent  P lanes  and  L inear  A pproxim ations  928
15.5   The Chain Rule       937
15.6   Directional Derivatives and the Gradient Vector       946
15.7   Maximum and Minimum Values            958
Applied Project - Designing a Dumpster  969
Discovery Project Quadratic Approximations and Critical Points  969
15.8   Lagrange Multipliers      970
Applied Project - Rocket Science  977
Applied Project - Hydro-Turbine Optimization  979
Review      980
Problems Plus   984
16     MULTIPLE INTEGRALS              986
16.1   Double Integrals over Rectangles       987
16.2   Iterated Integrals    995
16.3   Double Integrals over General Regions         1001
16.4   Double Integrals in Polar Coordinates       1010
16.5   Applications of Double Integrals       1016
16.6   Triple Integrals     1026
Discovery Project - Volumes of Hyperspheres  1036
167    Triple Integrals in Cylindrical Coordinates 1036
Discovery  Project - The  Intersection  of Three Cylinders  1041
16.8   Triple Integrals in Spherical Coordinates      1041
Applied  Project - Roller Derby  1048
16.9   Change of Variables in Multiple Integrals       1048
Review      1057
Problems Plus    1060
 17  VECTOR CALCULUS         1062
17.1  Vector Fields  1063
17.2  Line Integrals  1070
17.3  The Fundamental Theorem for Line Integrals  1081
17.4  Green's Theorem   1091
I 7.5  Curl and Divergence  1097
17.6  Parametric Surfaces and Their Areas  1106
17.7  Surface Integrals  1117
17.8  Stokes' Theorem  1128
Writing Project  Three Men and Two Theorems  1134
17.9  The Divergence Theorem  1135
17.10 Summary    1141
Review    1142
Problems Plus  145
"1 8 i  SECOND-ORDER DIFFERENTIAL EQUATIONS              146
18.1  Second-Order Linear Equations  1147
18.2  Nonhomogeneous Linear Equations  1153
8.3   Applications of Second-Order Differential Equations  1161
18.4  Series Solutions  1169
Review    1173
APPENDIXES       Al_
F     Proofs of Theorems  A2
G     Complex Numbers    AS
H     Answers to Odd-Numbered Exercises  A13



Library of Congress subject headings for this publication: Calculus