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TitleAdvanced Mathematics for Engineering
TagsDifferential Equations Derivative Equations Integral Ordinary Differential Equation
File Size27.2 MB
Total Pages898
Table of Contents
                            Cover Page
Title Page
ISBN 9812382917
PREFACE
CONTENTS (with page links)
	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

Advance d Mathematic s for

Engineering
_ . and

Science

Page 449

434 ADVANCED MATHEMATICS

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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