Forman S. Acton's 'Real Computing Made Real'
Forman S. Acton's Real Computing Made Real is now available from Dover, in paperback, at a reasonable price. This book is in some respects a follow-up to, and an amplication of the author's previous 'Numerical Methods That (usually) Work', but it stands on its own quite well. If you liked 'Numerical Methods', you'll like 'Real Computing' and learn some new things.
'Real Computing' ostensibly focuses on solving nonlinear equations and performing numerical integration, but the real value is in teaching how to recoginze difficult problems, and how to reformulate the problem to get a good answer. The pace is leisurely and thorough; not at all dry but rather engaging. This seems to offend readers who prefer a more pedantic presentation. Here's a sample:
AN EDUCATIONAL DALLIANCE
If you've never spent a numerical night with a robust alternating series, here's your chance! Compute sin(x) from
sin(x) = x - x^3/3! + x^5/5! - ...
Evaluate each term from its predecessor, summing as you go. Stop when you term shrinks to insignificance. Check your technique with x = 0.5 -- then go for x = 9.5 and x = 11. The experience seldom thrills but is very maturing -- especially if you are using a calculator with less than 10-digit precision.
To a calculator user of canned solvers and integrators, this book still offers much. It will teach you to recognize equations and integrals which are difficult to numerically solve quickly, accurately, or both. You will also learn some general methods to recast those nasty problems to get better results. 'Real Computing' is not an introduction to numerical methods nor is it a cookbook. Dover does in fact offer several good introductions:
A First Course in Numerical Analysis, Ralston & Rabinowitz
Numerical Methods, Dahlquist and Bjork
Introduction to Numerical Analysis, Hildbrand
Numerical Methods for Scientists and Engineers, Hamming
Acton devotes about thirty pages to sketching functions by hand. The motivation is to learn to really understand how the terms of a function affect its form, and to use that understanding to apply an appropriate algorithm or tranformation. However, much of that understanding could be acquired using the built-in function plotting features of graphing calculators.
(I have no business connection with Dover; just a happy repeat customer.)
'Real Computing' ostensibly focuses on solving nonlinear equations and performing numerical integration, but the real value is in teaching how to recoginze difficult problems, and how to reformulate the problem to get a good answer. The pace is leisurely and thorough; not at all dry but rather engaging. This seems to offend readers who prefer a more pedantic presentation. Here's a sample:
AN EDUCATIONAL DALLIANCE
If you've never spent a numerical night with a robust alternating series, here's your chance! Compute sin(x) from
sin(x) = x - x^3/3! + x^5/5! - ...
Evaluate each term from its predecessor, summing as you go. Stop when you term shrinks to insignificance. Check your technique with x = 0.5 -- then go for x = 9.5 and x = 11. The experience seldom thrills but is very maturing -- especially if you are using a calculator with less than 10-digit precision.
To a calculator user of canned solvers and integrators, this book still offers much. It will teach you to recognize equations and integrals which are difficult to numerically solve quickly, accurately, or both. You will also learn some general methods to recast those nasty problems to get better results. 'Real Computing' is not an introduction to numerical methods nor is it a cookbook. Dover does in fact offer several good introductions:
A First Course in Numerical Analysis, Ralston & Rabinowitz
Numerical Methods, Dahlquist and Bjork
Introduction to Numerical Analysis, Hildbrand
Numerical Methods for Scientists and Engineers, Hamming
Acton devotes about thirty pages to sketching functions by hand. The motivation is to learn to really understand how the terms of a function affect its form, and to use that understanding to apply an appropriate algorithm or tranformation. However, much of that understanding could be acquired using the built-in function plotting features of graphing calculators.
(I have no business connection with Dover; just a happy repeat customer.)
posted by db at 4:13 PM
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