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Tables of Contents for Multivariable Calculus
Chapter/Section Title
Page #
Page Count
11 FUNCTIONS OF SEVERAL VARIABLES
1
58
11.1 FUNCTIONS OF TWO VARIABLES
2
7
11.2 A TOUR OF THREE-DIMENSIONAL SPACE
9
5
11.3 GRAPHS OF FUNCTIONS OF TWO VARIABLES
14
9
11.4 CONTOUR DIAGRAMS
23
15
11.5 LINEAR FUNCTIONS
38
6
11.6 FUNCTIONS OF MORE THAN TWO VARIABLES
44
7
11.7 LIMITS AND CONTINUITY
51
5
REVIEW PROBLEMS
56
3
12 A FUNDAMENTAL TOOL: VECTORS
59
38
12.1 DISPLACEMENT VECTORS
60
8
12.2 VECTORS IN GENERAL
68
7
12.3 THE DOT PRODUCT
75
10
12.4 THE CROSS PRODUCT
85
8
REVIEW PROBLEMS
93
4
13 DIFFERENTIATING FUNCTIONS OF MANY VARIABLES
97
78
13.1 THE PARTIAL DERIVATIVE
98
7
13.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
105
5
13.3 LOCAL LINEARITY AND THE DIFFERENTIAL
110
8
13.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
118
10
13.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE
128
6
13.6 THE CHAIN RULE
134
8
13.7 SECOND-ORDER PARTIAL DERIVATIVES
142
4
13.8 PARTIAL DIFFERENTIAL EQUATIONS
146
8
13.9 NOTES ON TAYLOR APPROXIMATIONS
154
7
13.10 DIFFERENTIABILITY
161
8
REVIEW PROBLEMS
169
6
14 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA
175
40
14.1 LOCAL EXTREMA
176
8
14.2 GLOBAL EXTREMA: UNCONSTRAINED OPTIMIZATION
184
12
14.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS
196
12
REVIEW PROBLEMS
208
7
15 INTEGRATING FUNCTIONS OF MANY VARIABLES
215
58
15.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES
216
9
15.2 ITERATED INTEGRALS
225
10
15.3 TRIPLE INTEGRALS
235
4
15.4 NUMERICAL INTEGRATION: THE MONTE CARLO METHOD
239
4
15.5 DOUBLE INTEGRALS IN POLAR COORDINATES
243
5
15.6 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES
248
8
15.7 APPLICATIONS OF INTEGRATION TO PROBABILITY
256
9
15.8 NOTES ON CHANGE OF VARIABLES IN A MULTIPLE INTEGRAL
265
4
REVIEW PROBLEMS
269
4
16 PARAMETERIZED CURVES AND SURFACES
273
52
16.1 PARAMETERIZED CURVES
274
9
16.2 MOTION, VELOCITY, AND ACCELERATION
283
11
16.3 PARAMETERIZED SURFACES
294
12
16.4 THE IMPLICIT FUNCTION THEOREM
306
7
16.5 NOTES ON NEWTON, KEPLER, AND PLANETARY MOTION
313
6
REVIEW PROBLEMS
319
6
17 VECTOR FIELDS
325
16
17.1 VECTOR FIELDS
326
7
17.2 THE FLOW OF A VECTOR FIELD
333
5
REVIEW PROBLEMS
338
3
18 LINE INTEGRALS
341
44
18.1 THE IDEA OF A LINE INTEGRAL
342
9
18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES
351
7
18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS
358
9
18.4 PATH-DEPENDENT VECTOR FIELDS AND GREEN'S THEOREM
367
10
18.5 PROOF OF GREEN'S THEOREM
377
4
REVIEW PROBLEMS
381
4
19 FLUX INTEGRALS
385
26
19.1 THE IDEA OF A FLUX INTEGRAL
386
11
19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES
397
8
19.3 NOTES ON FLUX INTEGRALS OVER PARAMETERIZED SURFACES
405
4
REVIEW PROBLEMS
409
2
20 CALCULUS OF VECTOR FIELDS
411
50
20.1 THE DIVERGENCE OF A VECTOR FIELD
412
8
20.2 THE DIVERGENCE THEOREM
420
7
20.3 THE CURL OF A VECTOR FIELD
427
9
20.4 STOKES' THEOREM
436
7
20.5 THE THREE FUNDAMENTAL THEOREMS
443
5
20.6 PROOF OF THE DIVERGENCE THEOREM AND STOKES' THEOREM
448
7
REVIEW PROBLEMS
455
6
APPENDICES
461
24
A REVIEW OF LOCAL LINEARITY FOR ONE VARIABLE
462
1
B MAXIMA AND MINIMA OF FUNCTIONS OF ONE VARIABLE
463
1
C DETERMINANTS
464
1
D REVIEW OF ONE-VARIABLE INTEGRATION
465
6
E TABLE OF INTEGRALS
471
2
F REVIEW OF DENSITY FUNCTIONS AND PROBABILITY
473
10
G REVIEW OF POLAR COORDINATES
483
2
ANSWERS TO ODD NUMBERED PROBLEMS
485
12
INDEX
497