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An Introduction to Numerical Computation

Wen Shen
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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Drawing on ten years’ teaching, the author presents complete lecture notes and assignments for a semester’s introductory numerical methods course for senior undergraduates. Videos at the author's YouTube channel — from live lectures with short tutorials — augment the text, making it self-contained for self-study. Multivariable calculus, matrix basics, and some basic computer programming skills are the prerequisites here. The programming examples are in matlab. For a compact volume, the homework — homework, not exercises — is ample and well-conceived. Homework problems concluding each chapter include applications, programming tasks, and a list of items to turn in. A complete set of solutions is available for instructors upon request.

The book builds naturally from polynomial interpolation to numerical integration, linear systems, and approaches for ODEs and PDEs. The overview of Simpson’s Rule and variations and implications of the Trapezoid Rule are particularly ready to serve as “classroom capsules.” Considering future practitioners, I am glad to see consistent attention paid to error bounds, complexity and convergence theory. Some material is offered optionally, such as higher order splines.

I have some minor quibbles with the presentation. I feel the chapter on least squares belongs in the interpolation section, rather than interposed between linear systems and ODEs. The introduction to eigenvalues is particularly lacking in motivation and application when compared to the high standards set for other topics. Regardless, this is an excellent resource as a semester-long text, textbook adjunct, introduction for self-instruction, or a handy reference for practical implementations.

Tom Schulte has trained SQL server to support the gamma function through a numerical methods implementation and teaches at Oakland Community College in Michigan.

  • Computer Arithmetic
  • Polynomial Interpolation
  • Piecewise Polynomial Interpolation: Splines
  • Numerical Integration
  • Numerical Solution of Nonlinear Equations
  • Direct Methods for Systems of Linear Equations
  • Fixed Point Iterative Solvers for Linear Systems
  • The Method of Least Squares
  • Numerical Methods for ODEs
  • Two-Point Boundary Value Problems
  • FDM for Partial Differential Equations