Introduction to Numerical Analysis (Dover Books on Advanced Mathematics)

Rating:
Summary: Great book
Review: This book is really one of the best books on numerical analysis I've ever seen. It is simple but complete.

Rating:
Summary: Great bargain, still suitable as an introduction
Review: 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.