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Mathematical Theory of Finite Elements
This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course...
An Introduction to Partial Differential Equations with MATLAB
An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
Introduction to Quantum Control and Dynamics
The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental ph
Modeling and Control in Vibrational and Structural Dynamics
With numerous examples and exercises throughout, this book describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics. The text applies the differential geometric approach to waves, plates, shells, and quasilinear systems and describes differential geometric energy methods that are generalizations of classical energy methods. To make the book self-contained, the author gives an introduction to Riemannian geometry.
Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
Nonlinear Optimal Control Theory
Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
Stochastic Partial Differential Equations
As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and Itô's equations, highlighting several computational and analytical techniques. Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way. The author first brings the subject back to its root in classical concrete problems. He then discusses a ...
Mathematics of Quantum Computation and Quantum Technology
Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation an
Computational Electromagnetics
The dimmed outlines of phenomenal things all into one another unless we put on the merge focusing-glass of theory, and screw it up some times to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world James Clerk Maxwell (1831 - 1879) For a long time after the foundation of the modern theory of electromag netism by James Clerk Maxwell in the 19th century, the mathematical ap proach to electromagnetic field problems was for a long time dominated by the analytical investigation of Maxwell's equations. The rapid development of computing facilities during the last century has then necessitated appropriate numerical method...
