This research was divided into two parts which were contained in two Technical (Scientific) notes: (1) Technical Note No. 1. "Bounds for sums of reciprocals of eigenvalues". July, 1959. (2) Technical Note No. 2. "On the extrema of the frequencies of nonhomogeneous strings which equimeasurable density". December, 1959.

This research was divided into two parts which were contained in two Technical (Scientific) notes: (1) Technical Note No. 1. "Bounds for sums of reciprocals of eigenvalues". July, 1959. (2) Technical Note No. 2. "On the extrema of the frequencies of nonhomogeneous strings which equimeasurable density". December, 1959.

The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation

Well-known text uses a few basic concepts to solve such problems as the vibrating string, vibrating membrane, and heat conduction. Problems and solutions. 31 illustrations.

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.