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Numerical mathematics is a subtopic ofscientific computing. The focuslies on the efficiencyof algorithms, i.e. speed, reliability, and robustness.This leads to adaptive algorithms.The theoreticalderivation und analysesof algorithmsare kept as elementary as possible in this book; the neededsligtly advancedmathematical theory is summarized in the appendix.Numerous figures and illustrating examples explain the complex data, as non-trivial examples serve problems from nanotechnology, chirurgy, and physiology. The bookaddressesstudents as well aspractitioners inmathematics, naturalsciences, and engineering.It is designed as atextbook but also suitable for self study