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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.
Nonlinear Analysis
Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe is a collection of papers in honor of Erich H. Rothe, a mathematician who has made significant contributions to various aspects of nonlinear functional analysis. Topics covered range from periodic solutions of semilinear parabolic equations to nonlinear problems across a point of resonance for non-self-adjoint systems. Nonlinear boundary value problems for ordinary differential equations are also considered. Comprised of 14 chapters, this volume first discusses the use of fixed-point theorems in ordered Banach spaces to prove existence and multiplicity result for periodic solutions of semilinear parabolic differential equa...
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.
Variational Methods for Eigenvalue Approximation
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
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.
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.
Mathematical Analysis of Viscoelastic Flows
This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.
