Introduction to Numerical Analysis:
Second Edition (Dover Books on
Advanced Mathematics) by F. B.
Hildebrand
Great Bargain, Still Suitable As An Introduction
Well-known, respected introduction, updated to integrate concepts and
procedures associated with computers. Computation, approximation,
interpolation, numerical differentiation and integration, smoothing of data,
other topics in lucid presentation. 150 additional problems in this edition.
Bibliography.
Personal Review: Introduction to Numerical Analysis: Second
Edition (Dover Books on Advanced Mathematics) by F. B.
Hildebrand

This is a reprint of the 1974 2nd edition. So what is Numerical Analysis?
It's the down-and-dirty methods of approximation and interpolation of
equations that don't have closed-formed mathematical solutions. Just
about every real-world problem in material engineering from pipe flow,
wing design, convection currents to multivariate econometrics have to
resort to numerical approximations. You'll find all the familiar names from
your undergrad Math and Physics courses here (Newton, Gauss,
Largrange, etc.); however, advanced methods in Numerical Analysis has
changed tremendously since this book was published. Since NA is
dependent on present computing power, what was once too expensive or
unthinkable in the 70s can be done today. However, it's still a great
introduction and a great bargain from Dover. The writing style is informal
and conversationally peer-to-peer, rather than teacher-to-student. There is
no historic consciousness placing methods and men in context. You won't
find programming algorithms here (not even Fortran or Pascal). There are
probably better books out there for what ever your specific speciality is, but
at five times the price of this Dover reprint. You'll will find the old favorites
here. The book covers the various finite difference approximations
(forward, backward and central differences). It uses the operational
approach for these. The later chapters cover splines, continued fraction
and iterative methods. More importantly it covers the difference between
round-off error v. truncation of divergent series in approximations --
something that still confuses practicing professionals. Be warned there
have been many improvements in theory and methods in finite element
methods of Fluid Dynamics and other 3D modeling (bezier and NURBS);
And, the whole world of Complexity and Chaos theory happened well
AFTER this book was published. Calculus and Differential EQs are
prerequisite, there's no attempt at introduction in the text.
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