The book comprises ten chapters, Each chapter contains serveral soved problems clarifying the introduced concepts. Some of the examples are taken from the recent literature and serve to illustrate the applications in various fields of engineering and science. At the end of each chapter, there are assignment problems with two levels of difficulty. A list of references is provided at the end of the book. This book is the product of a close collaboration between two mathematicians and an engineer. The engineer has been helpful in pinpointing the problems which engineering students encounter in books written by mathematicians. Contents: Review of Calculus and Ordinary Differential Equations; Series Solutions and Special Functions; Complex Variables; Vector and Tensor Analysis; Partial Differential Equations I; Partial Differential Equations II; Numerical Methods; Numerical Solution of Partial Differential Equations; Calculus of Variations; Special Topics. Readership: Upper level undergraduates, graduate students and researchers in mathematical modeling, mathematical physics and numerical &computational mathematics.
From the Authors Introduction Diffusion is one of the few manageable nonequilibrium pro- cesses during which matter is transported through a system. Traditionally, diffusion is studied in physical chemistry; however, the fundamental understanding of diffusion processes is not possible without involving statistical physics. Diffusion in disordered systems, such as in polymers, has sometimes unexpected features, the nature of which has not yet been determined. Since modern technology involves more and more complex materials which rely on a subtle balance of microscopic effects, the understanding of diffusion processes in these materials is of paramount importance from the practical point of view. A renewed interest in the basic principles of diffusion is a direct result of new experimental data. This was a contributing factor in the preparation of this text. In the first chapter, the phenomenological thermodynamic basics of diffusion is reviewed, and the diffusion equation is derived from the principles of irreversible thermodynamics. The basic mathematical apparatus for solving diffusion equations is reviewed in the second chapter. The third chapter deals mainly with the vast amount of experimental data dealing with diffusion in polymers. . . . A reader interested in particular polymeric systems can use the . . . material as a useful introduction. The last chapter contains basic information concerning random walks and their application to the diffusion in disordered systems. The theory of random walks is widely used in polymer physics where it is usually combined with statistical mechanics to formulate various models of polymeric systems. Finally, useful mathematical formulas and references to the original sources of some mathematical methods are [provided] in the appendices. Some physical constants associated with several polymer solvent systems are also presented.
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
Describes the advances in the transport phenomena of particles, drops and bubbles in complex fluids. This book contains contributions from experts in areas such as particle deposition in membranes, flow of granular mixtures, food suspensions, foams, electro kinetic and thermo capillary driven flows, and two-phase flows.
This is a mathematical text suitable for students of engineering and science who are at the third year undergraduate level or beyond. It is a book of applicable mathematics. It avoids the approach of listing only the techniques, followed by a few examples, without explaining why the techniques work. Thus, it provides not only the know-how but also the know-why. Equally, the text has not been written as a book of pure mathematics with a list of theorems followed by their proofs. The authors' aim is to help students develop an understanding of mathematics and its applications. They have refrained from using clichés like “it is obvious” and “it can be shown”, which may be true only to a mature mathematician. On the whole, the authors have been generous in writing down all the steps in solving the example problems.The book comprises ten chapters. Each chapter contains several solved problems clarifying the introduced concepts. Some of the examples are taken from the recent literature and serve to illustrate the applications in various fields of engineering and science. At the end of each chapter, there are assignment problems with two levels of difficulty. A list of references is provided at the end of the book.This book is the product of a close collaboration between two mathematicians and an engineer. The engineer has been helpful in pinpointing the problems which engineering students encounter in books written by mathematicians.
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
A textbook of the history of the United States from its native inhabitants to the challenges of the present time, including cleaning the environment and solving the energy crisis.
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