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Numerical Methods in Engineering with MATLAB

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The second edition was largely precipitated by the introduction of anonymous functions into MATLAB. This feature, which allows us to embed functions in a program, rather than storing them in separate files, helps to alleviate the scourge of MATLAB programmers – proliferation of small files. In this edition, we have recoded all the example programs that could benefit from anonymous functions.

We also took the opportunity to make a few changes in the material covered:

• Rational function interpolation was added to Chapter 3.
• Brent’s method of root finding in Chapter 4 was replaced by Ridder’s method. The full-blown algorithm of Brent is a complicated procedure involving elaborate bookkeeping (a simplified version was presented in the first edition). Ridder’s method is as robust and almost as efficient as Brent’s method, but much easier to understand.
• The Fletcher–Reeves method of optimization was dropped in favor of the downhill simplex method in Chapter 10. Fletcher–Reeves is a first-order method that requires the knowledge of gradients of the merit function. Since there are few practical problems where the gradients are available, the method is of limited utility. The downhill simplex algorithm is a very robust (but slow) zero-order method that often works where faster methods fail.

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