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The Solution of Algebraic and Transcendental
7 other sections not shown
absolute error modulus accuracy algebraic applied approximation backward differences Bessel's formula binomial theorem boundary conditions calculation Chapter column consider convergence correction term D. R. Hartree decimal places derivative determined differencing differential equation digit estimate Evaluate Everett's formula example expression final finite difference five decimals forward difference four decimals fourth differences function values give given Gregory-Newton Hence interpolating polynomial interpolation formula inverse interpolation iterative Lagrangian linear interpolation necessary Newton-Raphson method Note numerical differentiation obtained operator pivotal values points possible quadratic factor quantities quartic equation quotient range reader real root recurrence relation relative error result rounding off error second differences second-order Section series solution significant figures Simpson's rule simultaneous equations six decimals Solve stage suitable synthetic division table of values tabular values tabulated Taylor expansion Taylor series theorem third differences three decimals tion trapezium rule truncated whence zero