Applied Analysis

Rating:
Summary: very fine but could be more advanced
Review: Lanczos' work is a fine, thorough text that covers most areas of advanced analysis in a readable style. His derivations are clear, his tangential explorations are absorbing, and he cites practical examples. The one area in which I find the book weak is harmonic functions, potential theory, and the applications of these to the calculus of resides. Consequently, the book is not "one-shop stopping" for all the mathematical techniques that an electrical engineer or physicist might require in his bag of tricks....

Rating:
Summary: Simply the best book on numerical analysis
Review: My dissertation advisor introduced me to this book over thirty years ago. I have since read it in its entirety twice and it is still the first book I consult when confronted with a new mathematical problem.

Lanczos's understanding of applied mathematics is very deep and he has a rare way of explaining things clearly yet concisely. I find his description of linear systems in terms of multidimensional coordinate systems, both orthogonal and skewed, to be the best anywhere. Also, his understanding and explanation of harmonic analysis (he invented the FFT after all) is worth the price of the book by itself.

Buy it, read it (at least once) then see if really need any other book on applied mathematics.

Rating:
Summary: If you don't want just recipes...
Review: Then this is the best book. Well, Hamming's is also so good! For Fourier analysis, and the taming of the Gibbs phenomenon, go straight to Lanczos. He knew it all, and was one of the inventors of the fast Fourier transform. This book is in the class of Sommerfeld's "Partial Differential Equations of Physics" and Lighthill's "Fourier Analysis and Generalizaed Functions". This is a very high compliment. Did you know he was also a first rate physicist, and a pioneer of quantum mechanics?

Rating:
Summary: If you don't want just recipes...
Review: Then this is the best book. Well, Hamming's is also so good! For Fourier analysis, and the taming of the Gibbs phenomenon, go straight to Lanczos. He knew it all, and was one of the inventors of the fast Fourier transform. This book is in the class of Sommerfeld's "Partial Differential Equations of Physics" and Lighthill's "Fourier Analysis and Generalizaed Functions". This is a very high compliment. Did you know he was also a first rate physicist, and a pioneer of quantum mechanics?

Rating:
Summary: Simply the best book on numerical analysis
Review: While this booked is dated because it was written for the days of mechanical calculators, it contains a great deal of very useful material. His discussion of Chebyeshev Polynomials one of the best I seen. His discussion on telescoping of power series is one of the few available. He gives great insight into a host of numerical methods. A very valuable work for the computer age as well.