Mathematical Formulas for Economists by Professor Dr. Bernd Luderer, Professor Dr. Volker Nollau, PDF

By Professor Dr. Bernd Luderer, Professor Dr. Volker Nollau, Dr. Klaus Vetters (auth.)

ISBN-10: 3540426167

ISBN-13: 9783540426165

ISBN-10: 3662124319

ISBN-13: 9783662124314

The current selection of formulation has been composed for college kids of economics or administration technology at universities, schools and exchange colleges. It comprises uncomplicated wisdom in arithmetic, monetary arithmetic and records in a compact and obviously prepared shape. This quantity is intended to be a reference paintings for use by way of scholars of undergraduate classes including a textbook, and by way of researchers wanting distinctive statements of mathematical effects. humans facing functional or utilized difficulties also will locate this assortment to be an effective and easy-to-use paintings of reference.

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Tq q ~ compound interest: tm continuous compounding: tm = In(Kl + .. , + Kk) -lnKo 8 ' 1 k 36 Mathematics of finance AllIlIliti(;o; Notations rate of interest term, number of payment intervals or rent periods periodic rent, size of each payment accumulation factor: q = 1 + ~ p n R q Basic formulas Basic assumption: Conversion and rent periods are equal to each other. Fdue = R . q . :L - present value of a perpetuity, payments at the beginning of each period =~ q-1 - present value of a perpetuity, interest used as earned q-1 n pdue n = ~ .

If the function f : D -+ R, D C lR is arbitrarily often differentiable at Xo ED, then the following power series is said to be the Taylor series formed at the point Xo: Taylor series • If f is arbitrarily often differentiable in a neighbourhood U of the point Xo and if the remainder in ~ Taylor's formula converges to zero for all x E U, then the Taylor series has a radius of convergence r > 0 and for x satisfying Ix - xol < r one has: f(x) f(n)( ) ,xo (x - xo)n n=O n. II +x 1 + ax + 1+ 1 1·2 aX - 3.

1 1 1 1 3 1 . 3 + 2 . 4 + ... + n(n + 2) + ... = 4" Function series An infinite series the terms of which are functions is called function series: h(x)+ h(x)+ ... k is the domain D of the function series. This series is called convergent for some value xED if the sequence {sn(x)} of partial sums converges to a limit s(x), otherwise it is called divergent. All xED for which the function series converges form the domain of convergence of the function series (it is assumed that the latter is equal to D).

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Mathematical Formulas for Economists by Professor Dr. Bernd Luderer, Professor Dr. Volker Nollau, Dr. Klaus Vetters (auth.)

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