Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus.
An extensive introduction outlines the uses and advantages of numerical integration and includes formulas and guides to orthogonal polynomials and specific integrals. Subsequent chapters explore approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Five helpful appendixes conclude the text.

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Methods of Numerical Integration

Davis, Philip J.; Rabinowitz, Philip

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