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Many mathematical models of physical, biological and social systems
involve partial differential equations (PDEs). The desire to
understand and influence these systems naturally leads to
considering problems of control and optimization. This book
presents important topics in the areas of control of PDEs and of
PDE-constrained optimization, covering the full spectrum from
analysis to numerical realization and applications. Leading
scientists address current topics such as non-smooth optimization,
Hamilton-Jacobi-Bellmann equations, issues in optimization and
control of stochastic partial differential equations, reduced-order
models and domain decomposition, discretization error estimates for
optimal control problems, and control of quantum-dynamical systems.
These contributions originate from the "International Workshop on
Control and Optimization of PDEs" in Mariatrost in October 2011.
This book is an excellent resource for students and researchers in
control or optimization of differential equations. Readers
interested in theory or in numerical algorithms will find this book
equally useful.
Functional analysis has become one of the essential foundations of
modern applied mathematics in the last decades, from the theory and
numerical solution of differential equations, from optimization and
probability theory to medical imaging and mathematical image
processing. This textbook offers a compact introduction to the
theory and is designed to be used during one semester, fitting
exactly 26 lectures of 90 minutes each. It ranges from the
topological fundamentals recalled from basic lectures on real
analysis to spectral theory in Hilbert spaces. Special attention is
given to the central results on dual spaces and weak convergence.
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