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Michael T. Heath’s Scientific Computing: An Introductory Survey is the textbook of choice for Numerical Analysis, Scientific Computing, or a 400-level Linear Algebra course. Note that this is only an introduction to Numerical Analysis; students looking for an in-depth resource will be disappointed at the broad overview given in Heath.
Scientific Computing is described in the first chapter, giving its historical origins, modern necessity, and a brief treatment of computational error. Thereafter, we leap straight into computation. Systems of linear equations, linear least squares, eigenvalues, non-linear equations, optimization, interpolation, integration and differentiation, initial and boundary value problems, partial differential equations, the fast fourier transform, and random numbers and simulation are the topics Heath covers, in 13 chapters.
A first semester’s introduction would cover chapters 1 through 6, up to optimization, saving the more salient advanced topics for a second semester’s discussion.
It’s the attention to detail that makes this book shine. Every chapter includes a historical anecdote at the end, tangentially describing the history and future of the techniques in that chapter. Examples are littered everywhere, and algorithms are set apart in special code boxes with line numbers. Matrices and vectors are set off in an easy to read bold typeface, while chapters are split up in sections that slowly progress from introduction to advanced algorithms, each section building on the contents of the previous. Homework questions are included after each chapter. My only complaint is that odd-numbered solutions are not included in the textbook, as is common in most other mathematics textbooks.
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction, it covers a broad range of material–enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
- Edition: Second
- Type: Hardcover
- ISBN: 0072399104
- Length: 563 pages
- Publisher: McGraw-Hill
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