1
Errata of the volume
M. Giaquinta, G. Modica, Mathematical Analysis. Functions of One Vari- able, Birkhauser, Boston, 2003.
In the next pages you will find the errata-corrige of the errors known to the authors up to now.
We will be very grateful to anybody who is willing to inform us about further errors or just misprints or would like to express criticism or other comments. Our e-mail addresses are
[email protected], [email protected]
Pisa and Firenze, September 14, 2005
Mariano Giaquinta
Giuseppe Modica
2
Page Error Correction
8
2e and
14
8is the equation is an equation
32
9Real valued Real-valued
57
5of sets of non-void sets
59
7explicit implicit
61
9sin a sin α
70
3,4halflines half-lines
80
13to Theorem 2.37
89
11M > 0 M > L
108
16,17se if
115
3spherae sphaera
118
17osc
J(f + g) osc
J(f g)
121
5se if
124
14any other differentiable any differentiable
132
7fractionary fractional
135
8spreadted spread
139
13sums. sum, see 3.81.
171
7y ∈ R y ∈ [−1, 1]
171
10 1+x(1+x2−2x2)3/221+x2−x2 (1+x2)3/2
178
12cost const
188
98(−t, t) ∩ (a, b) ] − t, t[∩]a, b[
189
15R
xc
f (x) dx int
cxf (x) dx 206
1− R
brar f(t)
t
= R
brar f(t)
t
dt
206
1log
ab.] log
bafor some r between ar and
br.]
3
210
15T
k−1(x; x
0) T
k−1(x)
213
12Taylors’ Taylor’s
228
5,6(5.10) . . . yields Lagrange’s theorem and the monotonicity of f
0yield for some x < ξ < x
0f (x
0) − f(x)
x
0− x = f
0(ξ) ≤ f
0(x
0), 228
9again . . . yields similarly we get
239
3,4,5x e x
239
7we infer we infer for x = (e x, e x, . . . , e x) 240
12 (2π)n/21 σn1 (2π)N/2σN
242
15= √
na
1· a
2· a
3· · · a
n= log √
na
1· a
2· a
3· · · a
n242
13→ √
na
1· a
2· a
3· · · a
n→ log √
na
1· a
2· a
3· · · a
n242
11→ √
na
1· a
2· a
3· · · a
n→ log √
na
1· a
2· a
3· · · a
n254
10R
T0
