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Applied Mathematics


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Introduction to Information Theory and Data Compression, Second Edition

Introduction to Information Theory and Data Compression, Second Edition

Peter D. Johnson, Jr., Greg A. Harris, D.C. Hankerson
February 26, 2003

An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed...

Continuum Models for Phase Transitions and Twinning in Crystals

Continuum Models for Phase Transitions and Twinning in Crystals

Mario Pitteri, G. Zanzotto
June 27, 2002

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material...

Spectral Computations for Bounded Operators

Spectral Computations for Bounded Operators

Mario Ahues, Alain Largillier, Balmohan Limaye
February 26, 2001

Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for...

Continuous Stochastic Calculus with Applications to Finance

Continuous Stochastic Calculus with Applications to Finance

Michael Meyer
October 25, 2000

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of...

Robust Computational Techniques for Boundary Layers

Robust Computational Techniques for Boundary Layers

Paul Farrell, Alan Hegarty, John M. Miller, Eugene O'Riordan, Grigory I. Shishkin
March 30, 2000

Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with...

Mathematical Models in Boundary Layer Theory

Mathematical Models in Boundary Layer Theory

O.A. Oleinik, V.N. Samokhin
May 25, 1999

Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles....

Weak and Measure-Valued Solutions to Evolutionary PDEs

Weak and Measure-Valued Solutions to Evolutionary PDEs

J. Necas, J. Malek, M. Rokyta, M. Ruzicka
May 01, 1996

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering...

Variational Theories for Liquid Crystals

Variational Theories for Liquid Crystals

E.G. Virga
May 15, 1995

Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past...

Asymptotic Treatment of Differential Equations

Asymptotic Treatment of Differential Equations

A. Georgescu
May 15, 1995

The main definitions and results of asymptotic analysis and the theory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity. Due...

Plasma Physics Theory

Plasma Physics Theory

A. Sitenko, V. Malnev
December 01, 1994

This book is an introduction to the field of modern plasma physics theory. The topics have been carefully chosen by the authors after many years teaching a graduate course in this subject. The book contains a comprehensive description of three widely used models in plasma physics: one-particle,...

Mathematical Modeling of Inelastic Deformation

Mathematical Modeling of Inelastic Deformation

J.F. Besseling, E. Van Der Giessen
May 15, 1994

Mathematical Modeling of Inelastic Deformation details the mathematical modeling of the inelastic behavior of engineering materials. The authors use a thermodynamic approach to the subject and focus on crystalline materials, but not to the exclusion of macro-moleular solids. Within a unified theory...

Vortex Structures in a Stratified Fluid: Order from Chaos

Vortex Structures in a Stratified Fluid: Order from Chaos

Sergey I. Voropayev, Y.D. Afanasyev
May 15, 1994

A fully systematic treatment of the dynamics of vortex structures and their interactions in a viscous density stratified fluid is provided by this book. The various compact vortex structures such as monopoles, dipoles, quadrupoles, as well as more complex ones are considered theoretically from a...

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