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An Introductory Guide to Computational Methods for the Solution of Physics Problems
This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They requi...
The Lost Promise
"Ellen Schrecker shows how universities shaped the 1960s, and how the 1960s shaped them. Teach-ins and walkouts-in institutions large and small, across both the country and the political spectrum-were only the first actions that came to redefine universities as hotbeds of unrest for some and handmaidens of oppression for others. The tensions among speech, education, and institutional funding came into focus as never before-and the reverberations remain palpable today"--
Structured Matrices in Mathematics, Computer Science, and Engineering II
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Hyperspherical Harmonics and Generalized Sturmians
This text explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory and generalized Sturmian basis functions. It also introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation.; The method of many-electron Sturmians offers an interesting alternative to the usual SCF-CI methods for calculating atomic and molecular structure. When many-electron Sturmians are used, and when the basis potential is chosen to be the attractive potential of the nuclei in the system, the following advantages are offered: the matrix representation of the nuclear attraction potential is diagonal; the kinetic energy term vanishes from the secular equation; the Slater exponents of the atomic orbitals are automatically optimized; convergence is rapid; a correlated solution to the many-electron problem can be obtained directly, without the use of the SCF approximation; and excited states can be obtained with good accuracy.; The text should be of interest to advanced students and research workers in theoretical chemistry, physics and mathematics.
Research in Progress
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Topics in Operator Theory
This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
