A Short Introduction to Numerical Analysis
This short book sets out the principles of the methods commonly employed in obtaining numerical solutions to mathematical equations and shows how they are applied in solving particular types of equations. Now that computing facilities are available to most universities, scientific and engineering laboratories and design shops, an introduction to numerical method is an essential part of the training of scientists and engineers. A course on the lines of Professor Wilkes's book is given to graduate or undergraduate students of mathematics, the physical sciences and engineering at many universities and the number will increase. By concentrating on the essentials of his subject and giving it a modern slant, Professor Wilkes has written a book that is both concise and that covers the needs of a great many users of digital computers; it will serve also as a sound introduction for those who need to consult more detailed works.
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accuracy Bessel's formula binomial coefficients boundary conditions calculation Cambridge Mathematical Tripos central differences coefficients column convenient conventional mathematical analysis convergence corrector corresponding curve decimal places degree less derivatives diagonal difference operators digital computer equivalent Everett's formula exact example expressed fictitious points finite difference formulae finite difference series first-order following formula fourth differences function values further terms given grid Hu Hn interpolation formula intersection interval Lagrange's 4-point formula Lagrangean form linear interpolation matrix multiply negligible Newton-Cotes formulae Newton-Gregory formula Newton-Raphson method number of points numerical analysis numerical integration obtain the following ordinary differential equations Poisson's equation polynomial of degree predictor range of integration residuals result root rounding errors Runge-Kutta method second differences Simpson's rule sinh step straight line taking h Taylor series third differences trapezoidal rule trial solution triangular true solution true value truncation error unwanted solution value of h vergence xu xn zero