Math 582BTopics in Numerical Analysis:
|
Textbook
U. M. Ascher and L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations, SIAM. $52.00 (SIAM Member Price: $36.40) [ Student membership is only $25: what a deal! ] (This is the main textbook for the class) |
|
(Recommended, if the online help & users' guide for Mathematica is insufficient) |
Software
Mathematica - all numerical assignments must be completed in Mathematica, which is available for use in the Mathematics Computer Lab. If you want to use Mathematica at home, you will need to buy your own copy.
|
References (not required)These are books you might what to look at for further reading if you find the textbook unsatisfactory in some area. You are not required or even expected to use these resources, but they are listed here in case you are interested. |
|
|
Butcher, J.C. (2003) Numerical Methods for Ordinary Differential Equations. Wiley. Quite a nice book, but a little to advanced and has more details on Runge-Kutta methods than I would like. But the author uses a bizarre chapter numbering scheme that seems straight out of some obscure governmental entity. Anyhow, the book is too expensive for me to consider recommending when there are much cheaper alternatives. From the publisher: $145, hardcover, or $25 per chapter for online/pdf access. |
Gear, G. William (1971) Numerical Initial Value Problems in Ordinary Differential Equations. Quite a nice book but dated and out of print. I just mention it because there are a large number of copies floating around the internet for $60 and up. Gear is one of the 20th century masters of the subject and the book is readable. |
Hairer. E & Norsett, S.P. (Volume 1, 2000) Solving Ordinary Differential Equations. Volume 1: Nonstiff Problems, and Hairer, E & Wanner, G (Volume 2, 2004) Volume 2: Stiff and Differential-Alagebraic Problems. An encyclopediac two volume text that covers everything about initial value problems. Advanced but quite readable. Printed by the yellow book people. This is the one to have in your library if you want impress people. (I have it in my library). There are a few 3rd world reprints floating on the internet and they are also not cheap. |
A. Isserles (1998) A First Course in the Numerical Analysis of Differential Equations, Cambridge. This book is not advanced enough for this class, and has a significant amount of material on partial differential equations. The material we will cover is in the first 100 pages of this book; the rest of the book deals with partial differential equations. Otherwise this is a nice book. From the publisher: List Price: $50 (paper); $120 (hard cover) |
J.D.Lambert (1995) Numerical Methods for Ordinary Differential Systems, Wiley. This book is too advanced for this class. Anyhow, I don't really like this book, the author seems intent on writing to obscure the subject. Naturally, this text is used in the equivalent course at UCLA. From the publisher: List Price: $110.00 |
L. F. Shampine (1994) Numerical Solution of Ordinary Differential Equations, Chapman and Hall. This book is at about the same level but is a bit wordy and not clearly organized. The author does not have a clear intent about what he wants to say and writes all around the subject without quite getting there. It is also significantly more expensive than our textbook.;] From the publisher: List Price: $109.95 |
General Reference on Numerical Analysis
Burden and Faires, Numerical Analysis. This is a general introduction to Numerical Analysis, and is used in Math 481A/B. In particular, chapter 5 gives an introduction to the material in this class. It is pricey. There are lots of (good) earlier editions online. From the publisher: 138.95 |
Further Reading in Ordinary Differential Equations
|
(More conscise; better treatment of theory) Driver, Rodney D. (1978) Introduction to Ordinary Differential Equations. Harper. A great introductory book, covers a lot of subjects in a small space. Actually a classic, I don't know why they never reprinted it. I think all the Harper & Row textbooks were lost when they merged with Collins because there doesn't seem to be much record of them. The only undergraduate book that I know of that even has a chapter on Delay equations. Lots of copies are available on the internet ranging from $10 to $150. |
(Theoretical) Hurewicz, Witold (1958) Lectures on Ordinary Differential Equations. MIT Press. A very cute little book (only 122 pages total). It's so good even the Dover reprint is out of print. But you can probably find a copy on the internet for around $5. |
