
This inexpensive paperback edition of a groundbreaking text stresses frequency approach in coverage of algorithms, polynomial approximation, Fourier approximation, exponential approximation, and other topics. Revised and enlarged 2nd edition.
The five key ideas from that book, enumerated by the author:
(1) the purpose of computing is insight, not numbers
(2) study families and relationships of methods, not individual algorithms
(3) roundoff error
(4) truncation error
(5) instability
Numerical Methods for Scientists and Engineers (1962)
Introduction To Applied Numerical Analysis (1971)
Digital Filters (1977)
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
After the first chapter I thought, "this guy is pretty sharp let's see what else he's written." That is when I found "You and Your Research".
You can watch him giving that 31-lecture course in 1995 here
https://www.youtube.com/playlist?list=PL2FF649D0C4407B30
Enjoy! It's wonderful. (The last lecture is the famous "You and Your Research" that he gave many times.)
I've really enjoyed his books too, from Numerical Methods for Scientists and Engineers to Methods of Mathematics Applied to Calculus, Probability, and Statistics. They're all drenched with experience.
[0] https://www.amazon.com/gp/aw/d/0486652416/
[1] http://alvand.basu.ac.ir/~dezfoulian/files/Numericals/Numeri...