Title Advanced Mathematics for Engineering Differential Equations Derivative Equations Integral Ordinary Differential Equation 27.2 MB 898
```                            Cover Page
Title Page
ISBN 9812382917
PREFACE
1 Review of Calculus and Ordinary Differential Equations
2 Series Solutions and Special Functions
3 Complex Variables
4 Vector and Tensor Analysis
5 Partial Differential Equations I
6 Partial Differential Equations II
7 Numerical Methods
8 Numerical Solution of Partial Differential Equations
9 Calculus of Variations
10 Special Topics
References
Appendices
Author Index
Subject Index
1 REVIEW OF CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS
2 SERIES SOLUTIONS AND SPECIAL FUNCTIONS
3 COMPLEX VARIABLES
4 VECTOR AND TENSOR ANALYSIS
5 PARTIAL DIFFERENTIAL EQUATIONS I
6 PARTIAL DIFFERENTIAL EQUATIONS II
7 NUMERICAL METHODS
8 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
9 CALCULUS OF VARIATIONS
10 SPECIAL TOPICS
REFERENCES
APPENDICES
AUTHOR INDEX
SUBJECT INDEX
A,B,C,D
E,F,G,H,I
J,K,L
M,N,O,P,Q,R,S
T,U,V,W,Z
STANDARD DERIVATIVES AND INTEGRALS
Back Cover Page
```
##### Document Text Contents
Page 2

Engineering
_ . and

Science

Page 449

y "

t = o

1 1 1 ^~
X

y J

t >o

X

FIGURE 5.4-2 Displacement of an initial pattern

Next we consider the case where f is zero and g is non-zero. Equation (5.4-26c) simplifies to

yx+ct

y(x,t) = ± I g(C)dC (5.4-32)
Jx-ct

The value of y at (x, t) depends only on the interval (x - c t) and (x + c t). This is the domain of
dependence and it is shown in Figure 5.4-3. It can be seen from Equation (5.4-26c) that the domain
of dependence is the same in the case f ^ 0.

Motivated by physical considerations, boundary and initial conditions [Equations (5.4-7a, b, 8a, b)]
have been imposed. These conditions are sufficient and necessary to determine a unique solution.

Page 450

PARTIAL DIFFERENTIAL EQUATIONS I 431

l x , t )

L A •
x-ct x+ct x

FIGURE 5.4-3 Domaine of influence

Diffusion Equation

Diffusion is a process by which matter is transported from one part of a system to another. Consider
the diffusion of chemical species A in a binary system of A and B. Under appropriate conditions,
Equation (A.IV-1) simplifies to

^ A = j c ,^ ^ A (5.4-33)
at 3x2

where cA is the concentration of A, &p& is the diffusivity, t is the time and x is the position.

For simplicity, we write Equation (5.4-33) as Equation (5.1-2) which is reproduced here for
convenience

i£ = a2— (5-1-2)
9t 3x 2

Equation (5.1-2) also describes the conduction of heat in an isotropic medium. In this case, c is the
temperature and a2 is the thermal diffusivity.

Page 897

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8
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