Methods in Numerical AnalysisMacmillan, 1964 - 408 páginas THE SUBJECT of numerical analysis has indeed prospered since the publication of the first edition of this book in 1956. Numerous books have been written. Some are on special topics in numerical analysis (for example, solutions of differential equations, system of linear equations, etc.); some are devoted to the mathematical theory in line with the current tendency to abstraction; others are concerned with programming for large-scale calculators; still others deal with advanced topics, ultramodern numerical analysis, or applications to specific sciences. All of these topics are important and must have a firm foundation. But the need for a basic, one-semester course at the undergraduate level with ample problems is even greater than before. The philosophy used in the creation of the first edition of this book is preserved in the revision in order to furnish the student with the fundamentals that permit him to progress to special and advanced topics and to the utilization of large computers. The second edition preserves the theme of the original book in the development of the classical numerical analysis with a minimum of mathematical background. Much of the material has been rewritten for greater clarity, and examples have been added. The major changes are: A] The analysis of empirical data which was formerly in Chapters 8 and 9 has been incorporated into one chapter and reorganized with additional elementary examples; n] a completely new chapter on linear programming has been added to provide an introduction to this important topic and its application to industrial problems; c] 86 new problems have been added. |
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a₁ a₁x A²y A²yo A³y accuracy Aitken's apply approximation b₁ b₂ binomial coefficients c₁ central difference table column computed constant convex polygon degree derived matrix determinant diagonal difference quotients differential equation divided differences elements entries equally spaced intervals evaluated Example Exercise expression Find the value given values independent variable inherent errors integral interpolating polynomial interpolation formula iteration k₁ k₂ Lagrange's formula Let us consider linear equations linear interpolation Mathematical multiplied Newton's formula normal equations notation numerical analysis obtain ORTHOGONAL POLYNOMIALS P₁ points polynomial interpolating problem procedure R₁ roots Runge-Kutta method S₁ S₂ schematic Simpson's rule SOLUTION solve Stirling's formula system of linear table of values tabulated functions tabulated values trigonometric trigonometric interpolation x₁ y₁ zero хо