Titlebook: Handbook of Mathematics; Ilja N. Bronshtein,Konstantin A. Semendyayev,Heine Book 20044th edition Springer-Verlag Berlin Heidelberg 2004 Al

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Geometry,. and . are not defined in today’s mathematics. We determine the relations between them only by axioms. We can imagine a . as a trace of a point moving in a plane along the shortest route between two different points without changing its direction.

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Linear Algebra,are systems of . times . elements, e.g., real or complex numbers, or functions, derivatives, vectors, arranged in . rows and . columns:

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Differentiation,The differential quotient of a function .=.(.) is equal to lim.if this limit exists and is finite.

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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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Vector Analysis and Vector Fields,A vector function of a scalar variable is a vector â whose components are real functions of .: ..

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Function Theory,Analogously to real functions, we can assign complex values to complex values, i.e., to the value . we can assign a complex number ., where . and . are real functions of two real variables. We then write .. The function . is a mapping from the complex . plane to the complex . plane.