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A First Course in Partial Differential Equations
Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.
Maximum Principles in Differential Equations
Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.
Navier-Stokes Equations and Nonlinear Functional Analysis
This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.
partial differential equations and applications
Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.
The CahnHilliard Equation: Recent Advances and Applications
This is the first book to present a detailed discussion of both classical and recent results on the popular CahnHilliard equation and some of its variants. The focus is on mathematical analysis of CahnHilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the CahnHilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Probabilistic Expert Systems
Probabilistic Expert Systems emphasizes the basic computational principles that make probabilistic reasoning feasible in expert systems. The key to computation in these systems is the modularity of the probabilistic model. Shafer describes and compares the principal architectures for exploiting this modularity in the computation of prior and posterior probabilities. He also indicates how these similar yet different architectures apply to a wide variety of other problems of recursive computation in applied mathematics and operations research. The field of probabilistic expert systems has continued to flourish since the author delivered his lectures on the topic in June 1992, but the understan...
Mathematical Aspects of Geometric Modeling
Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.
Stochastic Processes in the Neurosciences
This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Sequential Analysis and Optimal Design
An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.
