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Tables of Contents for First-Order Partial Differential Equations
Chapter/Section Title
Page #
Page Count
Preface
xi
Mathematical Preliminaries
1
30
Functions and Their Derivatives
1
2
Functions of Functions and Their Derivatives
3
3
Implicit Functions
6
3
Sets of Functions
9
4
Differentiation of Implicit Functions
13
2
Surfaces
15
2
Tangents and Normals
17
2
Direction Cosines and Space Curves
19
1
Directional Derivatives
20
1
Envelopes
21
5
Differential Equations
26
2
Strips
28
3
References
30
1
Mathematical Models That Give First-Order Partial Differential Equations
31
54
Introduction
31
2
Chromatography of a Single Solute
33
3
Chromatography of Several Solutes
36
3
Chromatography with Heat Effects
39
6
Countercurrent Adsorber
45
2
Heat Exchanger
47
2
Polymerization in a Batch Reactor
49
3
Other Problems in Chemical Kinetics
52
4
Tubular Reactor
56
2
Enhanced Oil Recovery
58
3
Kinematic Waves in General
61
4
Equations of Compressible Fluid Flow
65
2
Flow of Electricity and Heat and Propagation of Light
67
2
Two Problems in Optimization
69
5
An Estimation Problem
74
2
Geometrical Origins
76
3
Cauchy-Riemann Equations
79
6
References
80
5
Motivations, Classifications, and Some Methods of Solution
85
25
Comparisons Between Ordinary and Partial Differential Equations
85
3
Classification of Equations
88
4
When Has an Equation Been Solved?
92
2
Special Methods for Certain Equations
94
3
Method of Characteristics for Quasi-linear Equations
97
5
Alternative Treatment of the Quasi-linear Equations
102
8
References
108
2
Linear and Semilinear Equations
110
35
Linear and Semilinear Equations with Constant Coefficients
110
7
Examples of Linear and Semilinear Equations
117
6
Homogeneous Equations
123
6
Equilibrium Theory of the Parametric Pump
129
5
Linear Equations with Variable Coefficients
134
7
Linear Equations with n Independent Variables
141
4
References
144
1
Chromatographic Equations with Finite Rate Expressions
145
43
Solution by the Laplace Transformation
146
4
Linear Chromatography
150
11
Laplace Transformation as a Moment-generating Function
161
5
Chromatography with a Langmuir Isotherm
166
6
Fixed-bed Adsorption with Recycle
172
6
Poisoning in Fixed-bed Reactors
178
10
References
185
3
Homogeneous Quasi-linear Equations
188
53
Reducible Equations
189
5
Simple Waves
194
8
Equilibrium Chromatography of a Single Solute
202
11
Discontinuities in Solutions
213
8
Discontinuous Solutions in Equilibrium Chromatography
221
6
Water Flooding
227
6
Quasi-linear Equations with n Independent Variables
233
8
References
238
3
Formation and Propagation of Shocks
241
85
Formation of a Shock
242
9
Saturation of a Column
251
7
Development of a Finite Chromatogram
258
7
Propagation of a Pulse
265
9
Analysis of a Countercurrent Adsorber
274
11
Analysis of Traffic Flow
285
18
Theory of Sedimentation
303
23
References
322
4
Conservation Equations, Weak Solutions, and Shock Layers
326
85
Chromatographic Equations and Initial Data
328
3
Conservation Equations and the Jump Condition
331
5
Intermezzo on Convex Function and the Legendre Transformation
336
5
Weak Solutions and the Entropy Condition
341
9
Lax's Solution for the Quasi-linear Conservation Law
350
10
Some Additional Properties of Weak Solutions
360
10
Sound Waves of Finite Amplitude
370
9
Some General Properties of Chromatograms
379
3
Asymptotic Behavior
382
11
Shock-layer Analysis
393
18
References
404
7
Nonhomogeneous Quasi-linear Equations
411
72
Nonhomogeneous Equations with Two Independent Variables
412
13
Analysis of Transient Volumetric Pool Boiling
425
12
Black-box Steady State
437
15
Countercurrent Adsorber under Nonequilibrium Conditions
452
10
Countercurrent Adsorber with Reaction
462
21
References
481
2
Nonlinear Equations
483
32
Nonlinear Equations with Two Independent Variables
483
7
Geometry of the Solution Surface
490
6
Nonlinear Equations with n Independent Variables
496
2
Some Questions of Existence and Continuity
498
7
A Problem in Optimization
505
10
References
513
2
Variational Problems
515
20
Basic Problem of the Calculus of Variations
516
4
Canonical Form of the Euler Equations
520
3
Hamilton-Jacobi Equation
523
4
Equivalence of First-order Partial Differential Equations and Variational Problems
527
2
Principles of Fermat and Huygens
529
6
References
533
2
Author Index
535
4
Subject Index
539