Real Computing Made Real: Preventing Errors in Scientific and Engineering Calculations
Engineers and scientists who want to avoid insidious errors in their computer-assisted calculations will welcome this concise guide to trouble-shooting. Real Computing Made Real offers practical advice on detecting and removing bugs. It also outlines techniques for preserving significant figures, avoiding extraneous solutions, and finding efficient iterative processes for solving nonlinear equations.
Those who compute with real numbers (for example, floating-point numbers stored with limited precision) tend to develop techniques that increase the frequency of useful answers. But although there might be ample guidance for those addressing linear problems, little help awaits those negotiating the nonlinear world. This book, geared toward upper-level undergraduates and graduate students, helps rectify that imbalance. Its examples and exercises (with answers) help readers develop problem-formulating skills and assist them in avoiding the common pitfalls that software packages seldom detect. Some experience with standard numerical methods is assumed, but beginners will find this volume a highly practical introduction, particularly in its treatment of often-overlooked topics.
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accurate algebraic altho analytic answers approach approximation arctangent argument arithmetic asymptotes becomes chapter circle closed form converges correct cosh cosine cosine series cubic denominator deviation double root efﬁcient ellipse errors evaluate example exercise exponential expression factor ﬁgure ﬁnd ﬁrst Fortran fraction geometry give hence horizontal hyperbola inﬁnity integral integrand intersection larger limit logarithm look loss of significant nearly negative Newton Newton’s method numbers numerical quadratures ordinates origin pair parabola parallel geometry parameter plot pocket calculator positive power series precision problem produce pseudoconstant quadratic quadratic equation quadratures range real roots recurrence recurrence relations replace root-pairs shows signiﬁcant significant digits significant figures sine curve singular behavior sketch slightly slope small root solution solve square root starting values subtraction tangent point tanh thru tion transcendental equation transcendental function trapezoidal trouble unity usually vertical zero