Customer Reviews

Introduction to Numerical Analysis (Texts in Applied Mathematics, No 12)

5 star:		(1)
4 star:		(1)
3 star:		(2)
2 star:		(0)
1 star:		(2)

 

 

This text makes a decent reference book, but I find that the introduction of new ideas is not accompanied with sufficient explanation or motivation. I find myself continuously refering back to Burden and Faires, "Numerical Analysis" instead for more clear and concise descriptions of the same concepts. While our professor required the book for the course (because it is on the book list for qualifying exams), he rarely refers to it. I have accumulated about 5 numerical analysis books now, and I would recommend Burden and Faires, "Numerical Analysis" (7th edition) as the best for senior undergradute to 1st-year graduate level, as it has the best combination of theory, explanation, and examples. Stoer presents slightly more theoretical motivation to problems, which I think would be more interesting the second time around, but not as an 'Introduction'.

A classic. However this book is not a "cookbook" of numerical recipes, rather it places a strong emphasys in the numerical properties of algorithms. Good all-rounder and good sections on linear systems and interpolation. You'll probably want to complement this book with specialists on matrix computations, ODE, PDE and optimisation.

This book is decent as a reference book but it rather dense for someone who is learning the material the first time. (I'm using this book for a graduate course after having seen much of the material as an undergraduate and it's still a little difficult to read.)

It also has an inexcusable amount of typos in it. By the third edition, this really shouldn't be a problem.

This book is NOT an introduction!!

This book is NOT an introduction!!

If the portait of Mona Lisa is put 10 feet away in front of you, you see a beautiful picture. If the portait of Mona Lisa is put 2 inches away in front of you, you see chunks of paint. This book puts the portrait of Mona Lisa 2 inches away in front of you. As the result, you see chunks of paint.

If you are taught one thing each day, you learn one thing every day. After a year, you have learned 365 things. If you are taught 1000 things each day, you learn nothing every day, and after a year, you have learned nothing! This book tries to teach you 1000 things each day. As the result, you learn nothing.

Reading this book is a waste of time. The few things you can learn is not worth the confusion.

Yes, it might be a good reference. But for an introduction, find another book!

In the course of my graduate studies, I got lots of books in Numerical Mathematics. I read most of them, at least the chapters related to my work in Computer-Aided Design and Simulation of electronic circuits.
I have some of the books in several editions, as happens with this book from Stoer & Bulirsch (I have the 2nd and 3rd eds. of S&B). It isn't an easy read, and I remember having had some "viscous friction" in getting into the notation, a minor annoyment quickly surpassed. But when I had to jump into theorem proofs and fine tuning of algorithms, this book was the preferred. I recommend the chapters on Linear Systems, on solving Nonlinear Equations and on solving Ordinary Differential Equations, which I "used" a lot. This last 3rd edition already has some material about solving Linear Systems of equations with Krylov Space methods, such as GMRES.
As happens with many books, it can be complemented with texts offering a different point of view on Numerical Analysis. I recommend the classics from Hamming Numerical Methods for Scientists and Engineers, from Lanczos Applied Analysis, from Dahlquist and Bjork Numerical Methods, from Atkinson An Introduction to Numerical Analysis, and for electrical engineering CAD the excelent text from Vlach and Singhal Computer Methods for Circuit Analysis and Design (Electrical Engineering), (the old "Circuit Simulation Kama Sutra" from Chua and Lin, ISBN 0131654152, is no longer linkable, but deserves to be remembered here and should be reprinted, e.g by Dover books...). Of course the book from Press et al. Numerical Recipes 3rd Edition: The Art of Scientific Computing has its place, but due to the algorithm descriptions and organization, not to the code.
Compared with these texts, the book from S&B has the solid theory and sound foundation of the methods, as also has the book from Dahlquist which, however, is a bit dated. If you want a Numerical Analysis text that saves you from bad weather, at all times, get S&B from the Numerical Analysis German school which, in recent years gave us excellent texts on the solution of ODES, of DAEs and of PDEs in a broad range of science and engineering domains.

I endorse "Somebody"'s review:

"This book is NOT an introduction!!

This book is NOT an introduction!!

If the portait of Mona Lisa is put 10 feet away in front of you, you see a beautiful picture. If the portait of Mona Lisa is put 2 inches away in front of you, you see chunks of paint. This book puts the portrait of Mona Lisa 2 inches away in front of you. As the result, you see chunks of paint.

If you are taught one thing each day, you learn one thing every day. After a year, you have learned 365 things. If you are taught 1000 things each day, you learn nothing every day, and after a year, you have learned nothing! This book tries to teach you 1000 things each day. As the result, you learn nothing.

Reading this book is a waste of time. The few things you can learn is not worth the confusion.

Yes, it might be a good reference. But for an introduction, find another book!"

To which I responded:
"This book is being used for the Introduction to Numerical Analysis (Math 128A) course here at UC Berkeley for the Spring 2011 semester. This review paints the most accurate portrayal of why this book is such a failure for an introduction course. This is the first semester for which this book was used and our professor has recommended to all other professors to never use this book for future classes. It is absolutely horrific. I can definitely see how this would be an excellent reference book for people who have already, at one point, mastered this material.

I highly endorse "Somebody"'s review. If there is a professor reading these reviews and considering this book for their course, be warned. It's informally banned from here on out at UC Berkeley because it has been such a disaster of a book for an introduction course. It's simply ineffective and presents the material in a manner that is neither efficient nor effective for the beginning learner (for a class of upper division mathematics student who have mathematical maturity but no numerical analysis experience)."