In this seventh edition, we continue on the path established in previous editions. Quoting from the preface of the sixth edition, we “retain the same features that have made the book popular: ease of reading so that the instructor does not have to ‘interpret the book’ for the student, many illustrative examples that often solve the same problem with different procedures to clarify the comparison of methods, many exercises from which the instructor may choose appropriately for the class, more challenging problems and projects that show practical applications of the material.”
We have made substantial improvements on the previous edition. These include:
Theoretical matters that previously were in a separate section near the end of each chapter have been merged with the description of the procedures.
Example computer programs that admittedly were not of professional quality have been deleted, with the idea that this is not normally a programming course anyway. Easy-to-read algorithms have been retained so that students can write programs if they desire.
There is greater emphasis on computer algebra systems; MATLAB is the predominant system, but this is compared with Maple and Mathematica. The use of spreadsheets to solve problems is covered as well.
A new chapter on optimization (Chapter 7) has been added that includes multivariable cases as well as single-variable situations. Linear programming has been included, of course, but the treatment is intended to provide a real understanding of the simplex method rather than to merely give a recipe for solving the problem. Nonlinear programming is treated to contrast this with the simpler linear case.
Boundary value problems for ordinary diffferential equations have been separated from those for partial differential equations and are included in the chapter on ordinary differential equations. Partial differential equations that satisfy boundary conditions (elliptic equations) are combined with the other types of partial differential equations in a single chapter.
1. Solving Nonlinear Equations
2. Solving Sets of Equations
3. Interpolation and Curve Fitting
4. Approximation of Functions
5. Numerical Differentiation and Integration
6. Numerical Solution of Ordinary Differential Equations
8. Partial-Differential Equations
9. Finite-Element Analysis
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