First-order partial differential equations 阶偏微分方程

Written with engineering students in mind，this first volume of a highly regarded two-volume text is aimed at advanced undergraduates or first-year graduate students with a sound understanding of calculus and elementary ordinary differential equations．It Will also be of great value to mathematicians looking for a source of applications．
This volume--fully usable on its own--provides an extended treatment of the theory of first—order equations，along with applications and examples from a wide range of science and engineering disciplines．After going over the preliminaries．the authors discuss mathematical models that yield first-order partial differential equations；motivations．classifications．and some methods of solution；1inear and semilinear equations；chromatographic equations with finite rate expressions；homogeneous and nonhomogeneous quasilinear equations；formation and propagation of shocks；conservation equations．weak solutions．and shock layers；nonlinear equations；and variational problems．Exercises appear at the end 0f most sections．

Preface
0 Mathematical Preliminaries
0.1 Functions and Their Derivatives
0.2 Functions of Functions and Their Derivatives
0.3 Implicit Functions
0.4 Sets of Functions
0.5 Differentiation of Implicit Functions
0.6 Surfaces
0.7 Tangents and Normals
0.8 Direction Cosines and Space Curves
0.9 Directional Derivatives
0.10 Envelopes
0.11 Differential Equations
0.12 Strips
References
1 Mathematical Models That Give First.0rder Partial Differential Equations
1.1 Introduction
1.2 Chromatography of a Single Solute
1.3 Chromatography of Several Solutes
1.4 Chromatography with Heat Effects
1.5 Countercurrent Adsorber
1.6 Heat Exchanger
1.7 Polymerization in a Batch Reactor
1.8 Other Problems in Chemical Kinetics
1.9 Tubular Reactor
1.10 Enhanced Oil Recovery
1.11 Kinematic Waves in General
1.12 Equations of Compressible Fluid Flow
1.13 Flow of Electricity and Heat and Propagation of Light
1.14 TwO Problems in Optimization
1.15 An Estimation Problem
1.16 Geometrical Origins
1.17 Cauchy—Riemann Equations
References
2 Motivations.Classifications. and Some Methods of Solution
2.1 Comparisons Between Ordinary and Partial Differential Equations
2.2 Classification of Equations
2.3 When Has an Equation Been Solved?
2.4 Special Methods for Certain Equations
2.5 Method of Characteristics for Quasi—linear Equations
2.6 Alternative Treatment of the Quasi—linear Equations
References
3 Linear and Semilinear Equations
3.1 Linear and Semilinear Equations with Constant Coefficients
3.2 Examples of Linear and Semilinear Equations
3.3 Homogeneous Equations
3.4 Equilibrium Theory of the Parametric Pump
3.5 Linear Equations with Variable Coefficients
3.6 Linear Equations with n Independent Variables
References
4 Chromatographic Equations with Finite Rate Expressions
5 Homogeneous Quasi-linear Equations
6 Formation and Propagation of Shocks
7 Conservation Equation,Weak Solutions,and Shock Layers
8 Nonhomogeneous Quasi-linear Equations
9 Nonlinear Equations
10 Variational Problems
Author Index
Subject Index