A Practical Guide to Differential Geometry and the Shape Derivative
Many things around us have properties that depend on their shape - for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable". This approach, which is useful for understanding mathematical ......
Provides an introduction to computer benchmarking. Hockney includes material concerned with the definition of performance parameters and metrics and defines a set of suitable metrics with which to measure performance and units with which to express them. He also presents new ideas resulting from the application of dimensional analysis to the field ......
Surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging: Emphasizes mathematical techniques and ideas ......
A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing - the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore ......
Approximation techniques and variational principles represent vital tools for solving partial differential equations. This classic text introduces the reader to such solution methods at a level suitable for novices, before progressing through increasingly challenging problems. The book describes variational principles, including how to find them, ......
The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. As part of the ......
This book presents the first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for ......
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. This book focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the ......
This text provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science and engineering. The book covers the relevant mathematical ......
