pdfsharp c# : Change link in pdf file Library control API .net web page asp.net sharepoint TRENCH_REAL_ANALYSIS57-part278

562
AnswerstoSelectedExercises
Section6.3 pp. 414417
6:3:4
(p. 414)(a)
Œ1;=2
(b)
Œ1;2
(c)
Œ1;
(d)
Œ2
p
2;9=4
(e)
Œ
p
2;3=4
6:3:5
(p. 414)(a)
Œ1;3=2
(b)
Œ1;2
(c)
Œ1;
(d)
Œ2
p
2;7=4
(e)
Œ
p
2;5=4
6:3:6
(p.414)(b)
Letf.x/Dx.0x
1
2
/,f.x/Dx
1
2
.
1
2
<x1/;thenf is
locallyinvertiblebutnotinvertibleonŒ0;1.
6:3:7
(p.414)
F.S/D
˚
.u;v/
ˇ
ˇ
C2<arg.u;v/<C2
,whereisanargu-
mentof.a;b/;
F1
S
.u;v/D.u2Cv2/1=4
"
cos.arg.u;v/=2/
sin.arg.u;v/=2/
#
; 2<arg.u;v/<2C
6:3:10
(p. 415)(a)
x
y
D
1
10
u2v
3uC4v
; .F
1
/
0
D
1
10
1 2
3
4
(b)
2
4
x
y
´
3
5
D
1
2
2
4
uC2vC3w
uw
uCvC2w
3
5
; .F
1
/
0
D
1
2
2
4
1 2
3
1 0 1
1 1
2
3
5
6:3:12
(p.415)
G
1
.u;v/D
1
p
2
p
uCv
p
uv
,G
0
1
.u;v/D
1
2
p
2
1=
p
uCv
1=
p
uCv
1=
p
uv 1=
p
uv
G
2
.u;v/D
1
p
2
p
uCv
p
uv
,G0
2
.u;v/D
1
2
p
2
1=
p
uCv 1=
p
uCv
1=
p
uv 1=
p
uv
G
3
.u;v/D
1
p
2
p
uCv
p
uv
,G
0
3
.u;v/D
1
2
p
2
1=
p
uCv 1=
p
uCv
1=
p
uv 1=
p
uv
G
4
.u;v/D
1
p
2
p
uCv
p
uv
,G
0
4
.u;v/D
1
2
p
2
1=
p
uCv 1=
p
uCv
1=
p
uv
1=
p
uv
6:3:15
(p.416)
FromsolvingxDrcos,yDrsinforDarg.x;y/.Eachequation
issatisfiedbyanglesthatarenotargumentsof.x;y/,sincenoneoftheformulasidentifies
thequadrantof.x;y/uniquely.Moreover,
(c)
doesnotholdifxD0.
6:3:16
(p. 416)
x
y
DG.u;v/D.u2Cv2/1=4
"
cosŒ
1
2
arg.u;v/
sin.arg.u;v/=2/
#
,
whereˇ=2<arg.u;v/<ˇC=2andˇisanargumentof.a;b/;
G
0
.u;v/D
1
2.x2Cy2/
x y
y x
6:3:19
(p. 416)
IfF.x
1
;x
2
;:::;x
n
/D.x
3
1
;x
3
2
;:::;x
3
n
/,thenFisinvertible,but
JF.0/ D0.
6:3:20
(p. 416)(a)
A.U/D
1
1
1
25
5 5
3 8

uC5
v4
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AnswerstoSelectedExercises
563
(b)
A.U/D
1
1
C
1
6
4 2
3
3

u2
v3
(c)
A.U/D
2
4
0
1
1
3
5
C
2
4
0 1 1
1
1 0
1
0 0
3
5
2
4
u1
v1
w2
3
5
(d)
A.U/D
2
4
1
=2
3
5
C
2
4
0 1
0
1
0
0
0
0 1
3
5
2
4
u
vC1
w
3
5
6:3:21
(p. 417)
G
0
.x;y;´/D
2
6
6
6
6
4
coscos
sincos
sin
sin
rcos
cos
rcos
0
1
r
cossin 
1
r
sinsin
1
r
cos
3
7
7
7
7
5
6:3:22
(p. 417)
G0.x;y;´/D
2
6
6
6
4
cos
sin
0
1
r
sin
1
r
cos 0
0
0
1
3
7
7
7
5
Section6.4 pp. 431434
6:4:1
(p. 431)(a)
u
v
D
1
2
3
4
1 2

x
y
(b)
2
4
u
v
w
3
5
D
1
2
2
4
3 3
1 2
2 3
3
5
x
y
(c)
u
v
D
1
5
2 1
1
3

yCsinx
xCsiny
(d)
uDx,vDy,´Dw
6:4:3
(p. 431)
f
i
.X;U/D
0
@
Xn
jD1
a
ij
.x
j
x
j0
/
1
A
r
.u
i
u
i0
/
s
,1im,wherer
andsarepositiveintegersandnotalla
ij
D0.
(a)
rDs D3;
(b)
r D1,sD3;
(c)
rDsD2
6:4:4
(p. 431)
u
x
.1;1/D
5
8
,u
y
.1;1/D
1
2
6:4:5
(p. 431)
u
x
.1;1;1/D
5
8
,u
y
.1;1;1/D
9
8
,u
´
.1;1;1/D
1
2
6:4:6
(p. 431)(a)
u.1;2/D0,u
x
.1;2/Du
y
.1;2/D4
(b)
u.1;2/D2,u
x
.1;2/D1,u
y
.1;2/D
1
2
(c)
u.=2;=2/Du
x
.=2;=2/Du
y
.=2;=2/D0
(d)
u.1;1/D1,u
x
.1;1/Du
y
.1;1/D1
6:4:7
(p. 431)(a)
u
1
.1;1/D1,
@u
1
.1;1/
@x
D5,
@u
1
.1;1/
@y
D2
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564
AnswerstoSelectedExercises
u
2
.1;1/D2,
@u
2
.1;1/
@x
D14;
@u
2
.1;1/
@y
D2
(b)
u
k
.0;/D.2kC1/=2,
@u
k
.0;/
@x
D0,
@u
k
.0;/
@y
D1, kDinteger
6:4:8
(p. 432)
1
5
1 2 1
1 2 1
6:4:9
(p. 432)
u
0
.0/D3,v
0
.0/D1
6:4:10
(p. 432)
1
6
2
4
5
5
5 5
6
6
3
5
6:4:11
(p. 432)
U
1
.1;1/D
3
1
,U
0
1
.1;1/D
1 3
1 2
;
U
2
.1;1/D
3
1
,U
0
2
.1;1/D
1 3
1 2
6:4:12
(p. 432)
u
x
.0;0;0/D2,v
x
.0;0;0/Dw
x
.0;0;0/D2
6:4:13
(p. 433)
y
x
D
@.f;g;h/
@.x;´;u/
@.f;g;h/
@.y;´;u/
,y
v
D
@.f;g;h/
@.v;´;u/
@.f;g;h/
@.y;´;u/
x
D
@.f;g;h/
@.y;x;u/
@.f;g;h/
@.y;´;u/
,
´
v
D
@.f;g;h/
@.y;v;u/
@.f;g;h/
@.y;´;u/
,u
x
D
@.f;g;h/
@.y;´;x/
@.f;g;h/
@.y;´;u/
,u
v
D
@.f;g;h/
@.y;´;v/
@.f;g;h/
@.y;´;u/
6:4:14
(p. 433)
x D2yu,´ ´ D 2v;x D 2yu,v D
´
2
;y D
x
2
u
2
,
´D2v;yD
x
2
u
2
,vD
´
2
;´D2v,uDx2y;uDx2y,vD
´
2
6:4:15
(p. 433)
y
x
.1;1;2/D
1
2
,v
u
.1;1;2/D1
6:4:16
(p. 433)
u
w
.0;1/D
5
6
,u
y
.0;1/D0,v
w
.0;1/D
5
6
,v
y
.0;1/D0,
x
w
.0;1/D1,x
y
.0;1/D1
6:4:18
(p.434)
u
x
.1;1/D0,u
y
.1;1/D0,v
x
.1;1/D1,v
y
.1;1/D1,u
xx
.1;1/D
2,
u
xy
.1;1/D1,u
yy
.1;1/D2,v
xx
.1;1/D2,v
xy
.1;1/D1,v
yy
.1;1/D2
6:4:19
(p. 434)
u
x
.1;1/D0,u
y
.1;1/D
1
2
,v
x
.1;1/D
1
2
,v
y
.1;1/D0,
u
xx
.1;1/D
1
8
,u
xy
.1;1/D
1
8
,u
yy
.1;1/D
1
8
,v
xx
.1;1/D
1
8
,
v
xy
.1;1/D
1
8
,v
yy
.1;1/D
1
8
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Index
565
Section7.1 pp. 459462
7:1:2
(p.459)(a)
28
(b)
1
4
7:1:6
(p.460)
3.ba/.dc/,0 7:1:13
(p.460)
˚
.m;n/
ˇ
ˇ
m;nDintegers
Section7.2 pp. 480484
7:2:1
(p. 480)(a)
12
(b)
79
20
(c)
1
(d)
.1log2/=2
7:2:5
(p. 481)(a)
7
4
(b)
17
(c)
2
3
.
p
21/
(d)
1=4
7:2:7
(p. 481)(a)
3
8
,
5
8
(b)
3
8
,
5
8
7:2:8
(p. 482)(a)
3
4
,
5
4
(b)
3
4
´C
1
2
,
5
4
´C
1
2
(c)
´C
1
2
,1
7:2:11
(p. 482)(a)
285
(b)
0
(c)
0
(d)
1
4
.e
5
2
/
7:2:12
(p. 483)(a)
324
(b)
1
6
(c)
1
7:2:13
(p.483)
52
15
7:2:14
(p. 483)(a)
36
(b)
1
(c)
64
3
(d)
.e
6
C17/=2
7:2:17
(p. 483)(a)
2
27
(b)
1
2
.e
5
2
/
(c)
1
24
(d)
1
36
7:2:18
(p. 483)(a)
16
(b)
1
6
(c)
128
21
(d)
2
7:2:19
(p. 484)(a)
1
2
.b
1
a
1
/.b
n
a
n
/
P
n
jD1
.a
j
Cb
j
/
(b)
1
3
.b
1
a
1
/.b
n
a
n
/
P
n
jD1
.a2
j
Ca
j
b
j
Cb2
j
/
(c)
2
n
.b
2
1
a
2
1
/.b
2
n
a
2
n
/
7:2:20
(p. 484)
Rp
3=2
p
3=2
dx
R
p
1x
2
1=2
f.x;y/dy
7:2:22
(p.484)
1
2
Section7.3 pp. 514517
7:3:1
(p. 514)
LetS
1
andS
2
bedensesubsetsofRsuchthatS
1
[S
2
DR.
7:3:7
(p.514)(a)
1;c(constant);1 7:3:9
(p.515)
.u
2
u
1
/.v
2
v
1
/=jadbcj
7:3:10
(p. 515)
5
6
7:3:14
(p. 515)(a)
4
9
(b)
log
5
2
7:3:15
(p. 516)
3
7:3:16
(p. 516)
1
2
7:3:17
(p.516)
5
4
e.e1/
7:3:18
(p.516)
4
3
abc 7:3:19
(p.516)
2.e
25
e
9
/ 7:3:20
(p. 516)
16=3
7:3:21
(p. 516)
21=64
7:3:22
(p. 516)(a)
.=8/log5
(b)
.=4/.e
4
1/
(c)
2=15
7:3:23
(p. 517)
2a4=2
7:3:24
(p.517)(a)
1
˛
1
/.ˇ
n
˛
n
/=jdet.A/j 7:3:25
(p.517)
ja
1
a
2
a
n
jV
n
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Index
A
Abel’stest,219
Abel’stheorem,273,279
Absoluteconvergence,215
ofanimproperintegral,160
ofaseriesofconstants,215
ofaseriesoffunctions,247
Absoluteintegrability,160
Absoluteuniformconvergence,247,255
(Exercises4.4.17and4.4.20),
256(Exercise4.4.21)
ofapowerseries,257
Absolutevalue,2
Additionofpowerseries,267
Adjointmatrix,370
Affinetransformation,380
Alternatingseries,203
test,203,219
Analytictransformation,416(Exercise6.3.17)
Anglebetweentwovectors,286
Antiderivative,143,150(Exercise3.3.16)
Archimedeanproperty,5
Areaunderacurve,116
Argument,398
branchof,409,410,415(Exercise6.3.14)
Ascoli–Arzelatheorem,543
Associativelaws
fortherealnumbers,2(seep.1)
forvectoraddition,283
B
Besselfunction,277(Exercise4.5.11)
Binomialcoefficient,17(Exercise1.2.19),
102,194(Exercise4.1.35)
Binomialseries,266
Binomialtheorem,17(Exercise1.2.19)
Bolzano–Weierstrass theorem, 27, 294,
301(Exercise5.1.22)
Bound
lower,7
upper,3
Boundary,526
point,289,526
ofaset,23,289
Boundedconvergencetheorem,243
Boundedfunction,47,60,313
Boundednessofacontinuousfunction
onaclosedinterval,62,199
onacompactset,313
Boundedness ofanintegrablefunction,
119
onametricspace,537
Boundedsequence,181,197,292
Boundedset
above,3,313
below7,313
Boundedvariation,134135(Exercises3.2.7,
3.2.9,3.2.10)
Branch
ofanargument,409,415
ofaninverse,409
C
C[a,b],521
equicontinuoussubsetof,541
566
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Index
567
uniformlyboundedsubsetof,541
Cartesianproduct,31,435
Cauchyproductofseries,226,233(Ex-
ercise4.3.40),280(Exercise4.5.32)
Cauchysequence,527
Cauchy’sconvergencecriterion
forsequencesofrealnumbers,190
forsequencesofvectors,292
forseriesofrealnumbers,204
Cauchy’sroottest,215
Cauchy’suniformconvergencecriterion
forsequences,239
forseries,246
Chainrule,77,340,388
Changeofvariable,145,147
inanimproperintegral,164
inamultipleintegral,496
formulationoftherulefor,494
inanordinaryintegral,145,147
Changingtheorderofintegration,478
Characteristicfunction,70(Exercise2.2.9),
485
Closed
underscalarmultiplication,519
undervectoraddition,519
Closedinterval,23
Closedn-ball,291
Closedset,21,289,525
Closureofaset,23,289
Cofactor,370
expandingadeterminantin,371372
Commutativelaws
forthereals,2(Seep.1)
forvectoraddition,283
Compactset,20,293,537
Comparisontest
forimproperintegrals,156
forseries,206
Complementofaset,20
Completemetricspace,527
Completenessaxiom,4
Completeorderedfield,4
Componentfunction,311
Components,284(seep.281)
ofavector-valuedfunction,311,362
Compositefunction,58,311
continuityof,59,311
differentiabilityof,77,340
higherderivativesof,345
Taylorpolynomialof,109110
(Exercise2.5.11)
Compositionoffunctions,58
Conditionalconvergence
ofanimproperintegral,162
ofaseries,217
Conditionallyintegrable,162
Connectedmetricspace,549(Exercise8.3.2)
Connectedset,295
polygonally,296
Containmentofaset,19
Content,453
ofacoordinaterectangle,437
ofaset,485
zero,448,514(Exerciserefexer:7.3.2)
Continuity,54,302
ofacompositefunction,59,311
ofadifferentiablefunction,76,325
ofafunctionofnvariables,309
ofafunctionofonevariable,54
onaninterval,55
fromtheleft,54
ofamonotonicfunction,67
piecewise,56
fromtheright,54
onaset,56,311
ofasum,difference, product, and
quotient,57,311
intermsofsequences,198
ofatransformation,379
uniform,64,66,314,392(Exercise6.2.10)
ofauniformlimit,242
ofauniformlyconvergentseries,250
Continuousfunction54,309
boundednessof,62,313
extremevaluesofonaclosedinter-
val,62
integrabilityof,133
intermediatevaluesof,63,313
onametricspace,545
Continuoustransformation,379
568
Index
Continuouslydifferentiable,73,80,329,
385,409
Contractionmappingtheorem,547
Convergence
absolute
ofanimproperintegral,160
ofaseriesofconstants,215
absoluteuniform,247
conditional
ofaseries,217
ofanimproperintegral,162
ofanimproperintegral,152
ofaninfiniteseries,201
intervalof,258
pointwise
ofasequenceoffunctions,234,
238
ofaseriesoffunctions,244
ofapowerseries,257
radiusof,258
ofasequenceinametricspace,526
ofasequenceinR
n
,292
ofasequenceofrealnumbers,179
ofaseriesofconstants,200
ofasum,difference,orproductof
sequences,184
ofaTaylorseries,264
uniform,246
ofasequence,237
ofaseries,246
Coordinatecube,437
degenerate,437
nondegenerate,437
Coordinaterectangle,437
Coordinates,
polar,397,502,505
spherical,507
Covering,open,25,293,536
Cramer’srule,373
Criticalpoint,81,335
Curve,differentiable,453
D
Decreasingsequence,182
Dedekindcut,9(Exercise1.1.8)
Dedekind’stheorem,9(Exercise1.1.8)
Definedinductively,12
Degree
ofahomogeneouspolynomial,352
ofapolynomial,98
Deleted-neighborhood,22
Deletedneighborhood,525
Denseset,6,29(Exercise1.3.22),70(Ex-
ercise2.2.10)
Densityoftherationals,6,392(Esercise6.2.11)
Densityoftheirrationals,6
Denumerableset,176
Derivative,73
ofacompositefunction,77
directional,317
infinite,88(Exercise2.3.26)
ofaninversefunction,86(Exercise2.3.14)
left-hand,79
nth,73
one-sided,79
ordinary,317
partial,317
ofapowerseries,261262
right-hand,79
rthorder,319
second,73
ofasum,difference, product, and
quotient,77
zeroth,73
Determinant,368(seep.369)
expandingincofactors,371372
ofaproductofsquarematrices,370
Diameterofaset,292,586
Differencequotient,73
Differentiability
ofacompositefunction,340
continuous,329
ofafunctionofonevariable,73
ofafunctionofseveralvariables,323
ofthelimitofasequence,243
ofapowerseries,260262
ofaseries,252
Differentiable73,323
continuously,73,80,409
curve,453
Index
569
function,continuityof,76,325,385
onaninterval,80
onaset,73
surface,453
transformation,380
vector-valuedfunction,339
Differential,326
higher,348
ofalineartransformation,367
matrix,367,381
ofareal-valuedfunction,326
ofasum, difference, product,and
quotient,328
ofatransformation,381
Differentialequation,170171
(Exercises3.4.273.4.29)
Directionalderivative,317
Dirichlet’stest
forimproperintegrals,163
forseriesofconstants,217
foruniformconvergence ofseries,
248
Disconnectedset,295
Discontinuity
jump,56
removable,58
Discretemetric,519
Disjointsets,20
Distance
inametricspace,518
fromapointtoaset,301
(Exercise5.1.24)
betweensubsetsofametricspace,
549(Exercise8.3.3)
betweentwosets,301
(Exercise5.1.25)
betweentwovectors,283
Distributivelaw,2(seep.1)
Divergence,unconditional,233
(Exercise4.3.38)
Divergentimproperintegral,152
Divergentsequence,179
Divergentseries,201
Domainofafunction,31(seep.30),545
Doubleintegral,438
E
Edgelengthsofacoordinaterectangle,
437
Elementarymatrix,488
Emptyset,4
Entriesofamatrix,364
-neighborhood,21,289,525
-net,539
EquicontinuoussubsetofCŒa;b,541
Equivalentmetrics,530
Errorinapproximatingderivatives,112
(Exercises112112)
Euclideann-space,282(seep.281)
Euler’sconstant,230(Exercise4.3.14)
Euler’stheorem,357358(Exercise2.4.8)
Existenceofanimproperintegral,152
Existencetheorem,420
Expandingadeterminant,362372
Exponentialfunction,70(Exercise2.2.12),
72(Exercise2.2.33),228,273
Extendedmeanvaluetheorem,106
Extendedreals,7,
Exteriorpoint,289,526
Exteriorofaset,23,289,526
F
FaadiBruno’sformula,109
(Exercise2.5.11)
Fibonnaccinumbers,17(Exercise1.2.17)
Field
completeordered,4
ordered,2
properties,2(seep.1)
Finitereal,7
Firstmeanvaluetheoremforintegrals,
139
Forwarddifferences,104,71(Example2.2.18),
112(Exercises2.5.192.5.22)
Fredholm’sintegralequation,548
Function31,32
absolutelyintegrable,160
Bessel,277(Exercise277)
bounded,47,60,313
above,60,313
below,60,313
570
Index
ofboundedvariation,134(Exercise3.2.7)
characteristic,70(Exercise2.2.9),485
composite,58,311
decreasing,44
differentiableatapoint,73,323
domainof,31,32
exponential,70(Exercise2.2.12),72
(Exercise2.2.33),227,273
generating,278(Exercise4.5.26)
homogeneous,357(Exercise5.4.8)
increasing,44
infimumof,55,313
inverseof,68
linear,325
locallyintegrable,152
maximumof,60
monotonic,44,67
nondecreasing,44
nonincreasing,44
nonoscillatoryatapoint,162
nthpowerof,33
oscillationof,171
piecewisecontinuous,56
rangeof,31,32
rational,33,232,(Exercise4.3.28),
276(Exercise4.5.4)
real-valued,302
restrictionof,399
Riemannintegrable,114,438
Riemann–Stieltjesintegrable,125
strictlymonotonic,44
supremumof,313
valueof,31,32
vector-valued,311
Functions,
compositionof,58,311
differenceof,32
productof,32
quotientof,32
sumof,32
Fundamentaltheoremofcalculus,143
G
Generalizedmeanvaluetheorem,83
Generatingfunction,278(Exercise4.5.26)
Geometricseries,202
Groupingtermsofseries,220
H
Heine–Borelproperty,
Heine–Boreltheorem,172,66,172,293
Higherderivativesofacompositefunc-
tion,345
Higherdifferential,348
Homogeneousfunction,357(Exercise5.4.8),
359(Exercise5.4.23)
Homogeneouspolynomial,359(Exercise5.4.22),
Homogeneoussystem,375
Hypercube,295(seep.294)
Hölder’sinequality,521
I
Identitymatrix,370
Image,394
Implicitfunctiontheorem,420,423
Improperintegrability,146
Improperintegral,152
absolutelyconvergent,160
changeofvariablein,164
conditionallyconvergent,162
convergenceof,152
divergenceof,152
existenceof,152
ofanonnegativefunction,156
Incompletenessoftherationals,6
Increasingsequence,182
Indeterminateforms,91,9395
Inductionassumption,12
Inductionproof,12
Inequality,
Hölder,521
Minkowski,522
Schwarz,284
triangle,2,285
Infimum
ofafunction,60,313
ofaset,7
existenceanduniquenessof,7,9
(Exercise1.1.6)
Index
571
Infinitederivative,88(Exercise2.3.26)
Infinitelimits,42,306,317,316(Exercise5.2.6)
Infinitesequence,179
inametricspace,526
Infiniteseries,210,244
convergenceof,201
integrabilityof,251
oscillatory,201
Infinitynorm,496,523,524
Innerproduct,284
Instantaneous
rateofchange,74
velocity,74
Integrability
conditional,162
ofacontinuousfunction,133
ofafunctionofboundedvariation,
134(Exercise3.2.7)
improper,152
ofaninfiniteseries,251
local,152
ofamonotonicfunction,133
ofapowerseries,264
Integrable
Riemann,114,438
Riemann–Stieltjes,125
Integral
overanarbitrarysetinR
n
,452
ofaconstanttimesafunction,136,
456
double,439
improper,151
iterated,462
lower
forRiemannintegral,120,442
forRiemann–Stieltjesintegral128
(Exercise3.1.17)
multiple,439
ordinary,439
ofaproduct,138,456
proper,153
overarectangleinR
n
,436(Seep.435)
Riemann,114,438
Riemann–Stieltjes,125,127(Exer-
cise3.1.16),135(Exercises3.2.8
3.2.10),151(Exercise3.3.23)
oversubsetsofR
n
,436(Seep.435),
450,452,471472
ofasum,136,456
test,207
triple,439
Integrationbyparts,144
forRiemann–Stieltjesintegrals,135
(Exercise3.2.8)
Interiorofaset,21,289
Interiorpoint,21,289,525
Intermediatevaluetheorem
forcontinuousfunctions,63,313
forderivatives82
Intersectionofsets,20
Interval
closed,23
halfclosed,23
halfopen,23
open,21
semi-infinite,21,23
Intervalofconvergence,258
forderivatives,82
Inversefunction,68
branchof,409
derivativeof,86(Exercise.2.3.14)
ofafunctionrestrictedtoaset,399
ofamatrix,370
ofatransformation,396
Inversefunctiontheorem,412
Invertible,locally,400
Invertibletransformation,396
Irrationalnumber,6
Isolatedpoint,23,289,526
Iteratedintegral,462
Iteratedlogarithm,97(Example2.4.42),
167(Exercise3.4.10),208230
(Exercise4.3.11),230(Exercise4.3.16)
J
Jacobian,384,426
Jordancontent,485
changedbylineartransformation,488
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