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Reduced Basis Methods for Partial Differential Equations: An Introduction
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical prop…
- Edition
- -
- ISBN/ISSN
- 978-3-319-15431-2
- Collation
- -
- Series Title
- -
- Call Number
- 515.35
An Algebraic Geometric Approach to Separation of Variables
Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together …
- Edition
- Ed. 1
- ISBN/ISSN
- 978-3-658-11408-4
- Collation
- XII, 138
- Series Title
- -
- Call Number
- 516 SCH a
The Monge-Ampère Equation
Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas …
- Edition
- -
- ISBN/ISSN
- 978-3-319-43374-5
- Collation
- XIV, 216
- Series Title
- Progress in Nonlinear Differential Equations and Their Applications
- Call Number
- -
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint O…
All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construc…
- Edition
- -
- ISBN/ISSN
- 978-3-319-29535-0
- Collation
- XX, 237
- Series Title
- Operator Theory: Advances and Applications
- Call Number
- -
The Message of Quantum Science
In addition, whenever possible these essays take the opportunity to link foundational issues to the many exciting developments that are often linked to major experimental and technological breakthroughs in exploiting the electromagnetic field and in particular, its quantum properties and its interactions with matter, as well as to advances in solid state physics (such as new quantum Hall liquid…
- Edition
- -
- ISBN/ISSN
- 978-3-662-46422-9
- Collation
- XVIII, 348
- Series Title
- Lecture Notes in Physics
- Call Number
- -
New Challenges in Grid Generation and Adaptivity for Scientific Computing
This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related,…
- Edition
- 1
- ISBN/ISSN
- 978-3-319-06052-1
- Collation
- VIII, 325
- Series Title
- VIII, 325
- Call Number
- -
The Mathematics of Medical Imaging
Extending the ideas of the acclaimed first edition, new material has been adeed to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, new computer-based exerc…
- Edition
- -
- ISBN/ISSN
- 978-3-319-22665-1
- Collation
- XIV, 197
- Series Title
- Springer Undergraduate Texts in Mathematics and Technology
- Call Number
- -
Recollections of a Jewish Mathematician in Germany
Abraham A. Fraenkel was a world-renowned mathematician in pre–Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics. A friend of Albert Einstein, he knew many of the era’s acclaimed mathematicians personally. He moved to Israel (then Palestine under the British Mandate) in the early 1930s. In his autobiography Fraenkel describes his earl…
- Edition
- -
- ISBN/ISSN
- 978-3-319-30847-0
- Collation
- -
- Series Title
- -
- Call Number
- 510.9
The Mathematics Behind Biological Invasions
This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to in…
- Edition
- -
- ISBN/ISSN
- 978-3-319-32043-4
- Collation
- XVI, 362
- Series Title
- Interdisciplinary Applied Mathematics
- Call Number
- 510
The Mathematical Theory of Time-Harmonic Maxwell's Equations
This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpf…
- Edition
- -
- ISBN/ISSN
- 978-3-319-11086-8
- Collation
- XIII, 337
- Series Title
- -
- Call Number
- 510
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