Arithmetics -- Functions -- Geometry -- Linear Algebra -- Algebra and Discrete Mathematics -- Differentiation -- Infinite Series -- Integral Calculus -- Differential Equations -- Calculus of Variations -- Linear Integral Equations -- Functional Analysis -- Vector Analysis and Vector Fields -- Function Theory -- Integral Transformations -- Probability Theory and Mathematical Statistics -- Dynamical Systems and Chaos -- Optimization -- Numerical Analysis -- Computer Algebra Systems-Example Mathematica.

This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and  new paragraphs,  new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.