Titlebook: Economists‘ Mathematical Manual; Knut Sydsæter,Arne Strøm,Peter Berck Textbook 2005Latest edition Springer-Verlag Berlin Heidelberg 2005 S

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Volker Bach,Petra Vogler,Hubert ÖsterleDefinition of (global) maximum (minimum) of a function of . variables. As collective names, we use . points and values, or . points and values. Used to convert minimization problems to maximization problems.

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https://doi.org/10.1007/978-94-017-4358-7The .. A necessary condition for the solution of (16.1). An alternative form of the Euler equation. The .. A necessary condition for the solution of (16.1). Sufficient conditions for the solution of (16.1). . Adding condition (16.5) gives sufficient conditions.

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The Law Is My Friend, Philosopher and Guide,Definition of an . sequence. Boundedness conditions. . and . are given numbers. The . obtained from period . and onwards, given that the state vector is . at . = .. The . of problem (17.8). Properties of the value function, assuming that at least one of the boundedness conditions in (17.10) is satisfied.

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https://doi.org/10.1007/978-3-030-03347-7Definition of a linear combination of vectors. Definition of linear dependence and independence. A characterization of linear independence for . vectors in ℝ.. (See (19.23) for the definition of rank.) A characterization of linear independence for . vectors in ℝ.. (A special case of (18.4).)

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Set Theory. Relations. Functions,Let . be a relation from . to . and . a relation from . to .. Then we define the . . ○ . of . and . as the set of all (., .) in . × . such that there is an element . in . with . and .. . ○ . is a relation from . to ..

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Equations. Functions of one variable. Complex numbers,Let . be the number of changes of sign in the sequence of coefficients ., ., … , ., . in (2.8). The number of positive real roots of .(.) = 0, counting the multiplicities of the roots, is . or . minus a positive even number. If . = 1, the equation has exactly one positive real root.

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