Linear Differential Operators [Paperback]

Cornelius Lanczos (Author)

Book Description

Publication Date: July 10, 1997

This graduate-level, self-contained text addresses the basic and characteristic properties of linear differential operators, examining ideas and concepts and their interrelations rather than mere manipulation of formulae. Written at an advanced level, the text requires no specific knowledge beyond the usual introductory courses, and some 350 problems and their solutions are included.

Editorial Reviews

Review

'This scholarly volume describes Lanczos' life (1893-1974) and presents a clear development of the many fields he opened. ... a collection of seven photographs of Lanczos from 1910 to 1972 ... is followed by a fascinating twenty-eight page annotated story, 'Cornelius Lanczos: A Biographical Essay', by Barbara Gellai. The fortuitous inclusion of this excellent biography makes the Proceedings a more complete and desirable volume!' Mathematics of Computation --This text refers to an alternate Paperback edition.

Product Details

• Paperback: 576 pages
• Publisher: Dover Publications (July 10, 1997)
• Language: English
• ISBN-10: 0486680355
• ISBN-13: 978-0486680354
• Product Dimensions: 8.3 x 5.4 x 1.1 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,371,549 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

16 of 16 people found the following review helpful:

5.0 out of 5 stars A must!, May 18, 2000

By A Customer

This review is from: Linear Differential Operators (Paperback)

A very intuitive (geometrical) exposition of matrix calculus, adjoint problems, bilinear identity and Green's function (and more). If you really want to understand these concepts, read this masterpiece!

12 of 12 people found the following review helpful:

5.0 out of 5 stars Master Piece, November 22, 2007

By 

Bahram Houchmandzadeh (France) - See all my reviews
(REAL NAME)   

This review is from: Linear Differential Operators (Paperback)

As the other reviewers have said, this is a master piece for various reasons. Lanczos is famous for his work on linear operators (and efficient algorithms to find a subset of eigenvalues). Moreover, he has an "atomistic" (his words) view of differential equations, very close to the founding father's one (Euler, Lagrange,...).

A modern book on linear operators begins with the abstract concept of function space as a vector space, of scalar product as integrals,... The approach is powerful but somehow we loose our good intuition about differential operators.

Lanczos begins with the simplest of differential equations and use a discretization scheme (very natural to anybody who has used a computer to solve differential equations) to show how a differential equation transforms into a system a linear algebraic equation. It is then obvious that this system is undetermined and has to be supplemented by enough boundary condition to be solvable. From here, during the third chapters, Lanczos develops the concept of linear systems and general (n x m) matrices, the case of over and under determination, the compatibility conditions, ...

It is only after these discussions that he returns (chapter 4) to the function space and develops the operator approach and the role of boundary conditions in over and under-determination of solutions and the place of the adjoint operators. The remaining of the book develops these concepts : chp5 is devoted to Green's function and hermitian problems, chap7 to Sturm-Liouville,... The last chapter is devoted to numerical techniques, amazing if one think that the book was written at the very beginning of computers, which is a gem by itself.

18 of 21 people found the following review helpful:

5.0 out of 5 stars A joy to read., July 6, 1999

By A Customer

This review is from: Linear Differential Operators (Paperback)

Some mathematics and physics writers stand head and shoulders above the rest. Goldstein...Liboff...Morrison...Morse and Feshbach...and Lanczos. A joy to read, if you are both mathematically and verbally inclined.