The Mathematics of Diffusion

Author: John Crank

Publisher: Oxford University Press

ISBN: 9780198534112

Category: Mathematics

Page: 414

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Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

The Mathematics of Diffusion

Author: Wei-Ming Ni

Publisher: SIAM

ISBN: 9781611971972

Category: Heat equation

Page: 108

View: 6748

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Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical Lotka-Volterra competition systems. Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate.

An Introduction to the Mathematics of Biology: with Computer Algebra Models

Author: Edward K. Yeargers,James V. Herod,Ronald W. Shonkweiler

Publisher: Springer Science & Business Media

ISBN: 147571095X

Category: Mathematics

Page: 417

View: 3183

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Biology is a source of fascination for most scientists, whether their training is in the life sciences or not. In particular, there is a special satisfaction in discovering an understanding of biology in the context of another science like mathematics. Fortunately there are plenty of interesting (and fun) problems in biology, and virtually all scientific disciplines have become the richer for it. For example, two major journals, Mathematical Biosciences and Journal of Mathematical Biology, have tripled in size since their inceptions 20-25 years ago. The various sciences have a great deal to give to one another, but there are still too many fences separating them. In writing this book we have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own, in which both the biology and the math ematics should be equal and complete, and should flow smoothly into and out of one another. We have taught mathematical biology with this philosophy in mind and have seen profound changes in the outlooks of our science and engineering students: The attitude of "Oh no, another pendulum on a spring problem!," or "Yet one more LCD circuit!" completely disappeared in the face of applications of mathematics in biology. There is a timeliness in calculating a protocol for ad ministering a drug.

The Mathematics of Financial Derivatives

A Student Introduction

Author: Paul Wilmott,Sam Howison,Jeff Dewynne

Publisher: Cambridge University Press

ISBN: 1139810979

Category: Mathematics

Page: N.A

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Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant 'real-world' mathematics. In this book the authors describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation. A unified approach to modelling derivative products as partial differential equations is presented, using numerical solutions where appropriate. Some mathematics is assumed, but clear explanations are provided for material beyond elementary calculus, probability, and algebra. Over 140 exercises are included. This volume will become the standard introduction to this exciting new field for advanced undergraduate students.

Lectures on the Mathematics of Finance

Author: Ioannis Karatzas

Publisher: American Mathematical Soc.

ISBN: 9780821870099

Category: Business & Economics

Page: 148

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In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.

The Mathematics of Finite Elements and Applications

Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972

Author: J. R. Whiteman

Publisher: Academic Press

ISBN: 1483268845

Category: Mathematics

Page: 534

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The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

The Mathematics of Measurement

A Critical History

Author: John J. Roche,ROCHE

Publisher: Springer Science & Business Media

ISBN: 9780387915814

Category: Mathematics

Page: 330

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The Mathematics of Measurement is a historical survey of the introduction of mathematics to physics and of the branches of mathematics that were developed specifically for handling measurements, including dimensional analysis, error analysis, and the calculus of quantities.

The Mathematics of Finite Elements and Applications X (MAFELAP 1999)

Author: J.R. Whiteman

Publisher: Elsevier

ISBN: 9780080548685

Category: Technology & Engineering

Page: 432

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The tenth conference on The Mathematics of Finite Elements and Applications, MAFELAP 1999, was held at Brunel University during the period 22-25 June, 1999. This book seeks to highlight certain aspects of the state-of-the-art theory and applications of finite element methods of that time. This latest conference, in the MAFELAP series, followed the well established MAFELAP pattern of bringing together mathematicians, engineers and others interested in the field to discuss finite element techniques. In the MAFELAP context finite elements have always been interpreted in a broad and inclusive manner, including techniques such as finite difference, finite volume and boundary element methods as well as actual finite element methods. Twenty-six papers were carefully selected for this book out of the 180 presentations made at the conference, and all of these reflect this style and approach to finite elements. The increasing importance of modelling, in addition to numerical discretization, error estimation and adaptivity was also studied in MAFELAP 1999.

Mathematical Modeling of Earth's Dynamical Systems

A Primer

Author: Rudy Slingerland,Lee Kump

Publisher: Princeton University Press

ISBN: 9781400839117

Category: Science

Page: 248

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Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

The Mathematics of Reservoir Simulation

Author: Richard E. Ewing

Publisher: SIAM

ISBN: 0898716624

Category: Science

Page: 186

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This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

The Mathematics of the Bose Gas and its Condensation

Author: Elliott H. Lieb,Robert Seiringer,Jan Philip Solovej,Jakob Yngvason

Publisher: Springer Science & Business Media

ISBN: 3764373377

Category: Science

Page: 208

View: 2789

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This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.

The Mathematics of Combustion

Author: John D. Buckmaster

Publisher: SIAM

ISBN: 0898710537

Category: Mathematics

Page: 254

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Explores the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact.

An Introduction to the Mathematics of Financial Derivatives

Author: Salih N. Neftci

Publisher: Elsevier

ISBN: 0080478646

Category: Business & Economics

Page: 527

View: 414

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An Introduction to the Mathematics of Financial Derivatives, Second Edition, introduces the mathematics underlying the pricing of derivatives. The increased interest in dynamic pricing models stems from their applicability to practical situations: with the freeing of exchange, interest rates, and capital controls, the market for derivative products has matured and pricing models have become more accurate. This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives. This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.

Diffusion-Wave Fields

Mathematical Methods and Green Functions

Author: Andreas Mandelis

Publisher: Springer Science & Business Media

ISBN: 9780387951492

Category: Science

Page: 741

View: 7119

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Develops a unified mathematical framework for treating a wide variety of diffusion-related periodic phenomena in such areas as heat transfer, electrical conduction, and light scattering. Deriving and using Green functions in one and higher dimensions to provide a unified approach, the author develops the properties of diffusion-wave fields first for the well-studied case of thermal-wave fields and then applies the methods to nonthermal fields.

The Mechanisms of Fast Reactions in Solution

Author: Edward Caldin

Publisher: IOS Press

ISBN: 9781586031039

Category: Technology & Engineering

Page: 329

View: 527

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This text deals with the contribution of fast reaction techniques to our understanding of events on the molecular scale during chemical reactions. It covers the advances resulting from the combination of chemical kinetic and spectroscopic methods and highlights the information to be obtained from ultrafast processes lasting a few picoseconds or less. Computerized molecular dynamics calculations are shown to be an additional important tool. These methods have transformed the extent of detail of knowledge it is now possible to obtain of individual reaction mechanisms. The book contains sections on: the rates of diffusion-controlled reactions, the mathematical theory of diffusion and diffusion-controlled reaction rates, flash-photolysis techniques, initiation by high-energy radiation: plus radiolysis, fluorescence quenching and energy-transfer from excited molecules, ultrafast processes: sub-picosecond and femtosecond techniques, proton-transfer and group-transfer reactions in solution: Marcus theory (I) and electron-transfer reactions: Marcus theory (II).

Analytical Heat Diffusion Theory

Author: A Luikov

Publisher: Elsevier

ISBN: 0323143229

Category: Science

Page: 702

View: 9500

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Analytical Heat Diffusion Theory is a revised edition of an earlier book by Academician Luikov, which was widely used throughout the Soviet Union and the surrounding socialist countries. This book is divided into 15 chapters that treat heat conduction problems by the classical methods and emphasize the advantages of the transform method, particularly in obtaining short time solutions of many transient problems. This book starts with a discussion on the physical fundamentals, generalized variables, and solution of boundary value problems of heat transfer. Considerable chapters are devoted to the basic classical heat transfer problems and problems in which the body surface temperature is a specified function of time. Other chapters explore the heat transfer problems under different heat sources, including continuous and pulse-type. The discussion then shifts to the problem of freezing wet ground, two-dimensional temperature field, and heat conduction with variable transfer coefficients. The final chapters deal with the fundamentals of the integral transforms and their application to heat conduction problems. These chapters also look into the application of the theory of analytic functions to the heat conduction theory of mathematical physics. This book is an invaluable source for advanced undergraduate or graduate in analytical heat transfer.