Titlebook: Handbook of Mathematics; I.N. Bronshtein,K.A. Semendyayev,Heiner Mühlig Book 2015Latest edition Springer-Verlag Berlin Heidelberg 2015 Ana

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Algebra and Discrete Mathematics,A . is the mental reflection of a fact, expressed as a sentence in a natural or artificial language. Every proposition is considered to be true or false.

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Differential Equations,. is an equation, in which one or more variables, one or more functions of these variables, and also the derivatives of these functions with respect to these variables occur. The . of a differential equation is equal to the order of the highest occurring derivative.

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Calculus of Variations,A very important problem of the differential calculus is to determine for which . values the given function .(.) has extreme values. The calculus of variations discusses the following problem: For which functions has a certain integral, whose integrand depends also on the unknown function and its derivatives, an extremum value?

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Linear Integral Equations,An integral equation is an equation in which the unknown function appears under the integral sign. There is no universal method for solving integral equations. Solution methods and even the existence of a solution depend on the particular form of the integral equation.

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Function Theory,Analogously to real functions, complex values can be assigned to complex values, i.e., to the value . = . + i . one can assign a complex number . = . + i ., where . = .(.) and . = .(.) are real functions of two real variables. This relation is denoted by . = .(.). The function . = .(.) is a mapping from the complex . plane to the complex . plane.

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