... N(m
2
,σ
2
2
), then
X + Y is N(m
1
+ m
2
,σ
2
1
+ σ
2
2
).
To see this, just calculate
φ
X+Y
(λ)=φ
X
(λ)φ
Y
(λ)=e
−im
1
λ−
λ
2
σ
2
1
2
e
−im
2
λ−
λ
2
σ
2
2
2
= e
−i(m
1
+m
2
)λ−
λ
2
2
(σ
2
1
+σ
2
2
)
.
22
G. ... conditional expectation. Let us take the linear space L
2
(Ω) = L
2
(Ω, U), which consists
of all real-valued, U–measurable random varia...
... N(m
2
,σ
2
2
), then
X + Y is N(m
1
+ m
2
,σ
2
1
+ σ
2
2
).
To see this, just calculate
φ
X+Y
(λ)=φ
X
(λ)φ
Y
(λ)=e
−im
1
λ−
λ
2
σ
2
1
2
e
−im
2
λ−
λ
2
σ
2
2
2
= e
−i(m
1
+m
2
)λ−
λ
2
2
(σ
2
1
+σ
2
2
)
.
22
G. ... conditional expectation. Let us take the linear space L
2
(Ω) = L
2
(Ω, U), which consists
of all real-valued, U–measurable random varia...
... Introduction 22 6
9 .2 First-order equations 22 6
9.3 Classification of second-order equations 22 8
9.4 The wave equation in
R
2
and R
3
23 4
9.5 The eigenvalue problem for the Laplace equation 24 2
9.6 Separation ... x
L
,λ
n
=
nπ
L
2
n = 1, 2, 3,
Recall from linear algebra that an eigenvalue has multiplicity m if the space
consisting of its eigenvectors is m-dimensi...
... Function 42
2.1 .2 Smoothness of the Solution 43
2. 1.3 A Maximum Principle 44
2. 2 A Finite Difference Approximation 45
2. 2.1 Taylor Series 46
2. 2 .2 A System of Algebraic Equations 47
2. 2.3 Gaussian Elimination ... Series 25 2
8.1.3 The Complex Form 25 5
xiv Contents
8.1.4 Changing the Scale 25 6
8 .2 Boundary Value Problems and Orthogonal Functions 25 7
8 .2. 1 Other Bound...
... FTCS algorithm is also an example of
a single-level scheme, since only values at time level n have to be stored to find
values at time level n +1.
von Neumann Stability Analysis
Unfortunately, equation ... ed.
(New York: Wiley-Interscience). [1]
Centrella, J., and Wilson, J.R. 1984,
Astrophysical Journal Supplement
, vol. 54, pp. 22 9 24 9,
Appendix B. [2]
Hawley, J.F., Smarr, L. L., an...
... http://www.nr.com or call 1-8 0 0-8 7 2- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).
y(x)
1
2
x
1
x
2
x
3
x
Figure 16.1.1. Euler’s method. In this simplest (and least accurate) ... 1980,
Introduction to Numerical Analysis
(New York: Springer-Verlag),
Chapter 7.
Lambert, J. 1973,
Computational Methods in Ordinary Differential Equa...