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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_12” 2011/5/23 1:04 page 50 #50
12-50 Real Analysis
Theorem 12.8.22 (Stoke’s Theorem) Let be a well-behaved sur-
face whose boundary is a curve ∂.IfA(x, y, z), B(x, y, z), C(x, y, z)
C
(), then

(C
y
B
z
)dy dz + (A
z
C
x
)dz dx + (B
x
A
y
) dxdy
=
∂
Adx+ Bdy+ Cdz.
Theorem 12.8.23 (Gauss Divergence Theorem) Let S be a well-
behaved region in
R
3
whose boundary S is a closed surface. Let
A(x, y, z), B(x, y, z), C(x, y, z) C
(S). Then

S
(A
x
+B
y
+C
z
)dx dy dz =

S
A dydz +B dzdx+C dxdy.
SOLVED EXERCISES
1. Examine whether the following limit exists.
lim
(x,y)(0,0)
|y |
|x|
x
2
+ y
2
x
2
+ y
2
+
y
x
Solution: We shall show that the limit does ...
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Publisher Resources

ISBN: 9781299447561Publisher Website