Numerical Methods for Engineers and Scientists Hardcover – 1 Mar 1992
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"a good, solid instructional text on the basic tools of numerical analysis." -AIAA Journal --This text refers to an alternate Hardcover edition.
Most Helpful Customer Reviews on Amazon.com (beta)
The good points are
1. Each method described comes with a index notated formula that takes the head ache out of programming. Plus there are plenty of FORTRAN subroutines to look at.
2. Not only does Hoffman give you the finite difference equation he also throws in a solved example with one or two iterations worked out in full detail; the benefit of this cannot be overstated.
3. Plenty of practice problems with results at the back of the book.
4. Enough math to give the reader an insight into how the method works. If you care for rigor this is not the book.
The drawbacks are
1. Hoffman has condensed the portions dealing with PDE's from previous editions cutting out some theoretical development. Since most wouldn't have had a course in PDE's (like me) a few more pages might have better squared away a few difficult concepts (eg. characteristic lines of PDE's).
2. Could use another round of proof-reading. This book is littered with typos; which one runs into even in key formulas. This is unacceptable in what is otherwise a pedagogically sound book.
3. I would have liked to see some more elaboration on multidimensional problems in PDE's apart from the 1D unsteady examples which form the workhorse. Hoffman mentions that the explicit methods for 1D unsteady problems work for higher while the implicit schemes introduce numerical complexity which merit advanced methods. These specialized methods for higher dimensional parabolic and hyperbolic PDE's are not developed. As it stands the book is packed with enough material for 3 semesters study.
This book works well for self study. Everything from linear algebra (direct and iterative methods, LU factorization, eigenproblems), non-linear eqns, interpolation, numerical integration and differentiation, ODE's, BVP's, and PDE's is touched upon. Unlike most introductory texts Hoffman doesn't shy away from non-linear problems in differential equations.
I used it for the num. methods course even though the prescribed text was Heath's Scientific Computing which was the worst textbook I ever read (thankfully never purchased it). If you are getting started in CFD then this book provides a solid first step.
But keep in mind one feature (not drawback). This book uses heavily finite difference method (400 pages in the 1st edition and 200 pages in the 2nd). This method is good for only 1d problems. Coordinate transformation needed to extend this to 2d or 3d (even just non-uniform 1d) is not easy especially for 3d. I wish there was an equally good book on finite volume method, which is popular for 3d CFD. Anyways, this book is intended for beginners and thus the choice of finite difference method is an appropriate one.
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