Cornelius Lanczos - Böcker

Philosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.

Don't let the title fool you! If you are interested in numerical analysis, applied mathematics, or the solution procedures for differential equations, you will find this book useful. Because of Lanczos's unique style of describing mathematical facts in nonmathematical language, Linear Differential Operators also will be helpful to nonmathematicians interested in applying the methods and techniques described.Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems.Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: ""What are the basic and characteristic properties of linear differential operators?""In the author's words, this book is written for those ""to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field.

To quote a review by W. Ledermann in the Physics Bulletin, 'By skilfully blending the points of view of pure and applied mathematics, of physics, and of numerical methods, Professor Lanczos has succeeded in writing a book on Fourier series which is highly readable and informative. The subject itself is used as a leitmotiv to illuminate and revise the fundamental concepts of analysis ranging from the notion of a function to the method of contour integration.' Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. The author meticulously develops the topic in a friendly, conversational tone to clarify the material and engage the reader. 161 problems are integrated into the text to walk undergraduate and graduate students of engineering, physics, and mathematics down the simplest path to a solution.