Numerical Methods in Computational Finance. Daniel J. Duffy
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Название: Numerical Methods in Computational Finance
Автор: Daniel J. Duffy
Издательство: John Wiley & Sons Limited
Жанр: Ценные бумаги, инвестиции
isbn: 9781119719724
isbn:
A simple example of use is:
More challenging examples of composite functions are:
1.3.1 Taylor's Theorem
Taylor's theorem allows us to expand a function as a series involving higher-order derivatives of a function. We take the Cauchy form (with exact remainder):
(1.10)
and:
We conclude with a discussion of the exponential function. It is the only function that is the same as its derivative. To see this, we use the formal definition (1.7) of a derivative (and noting that
We summarise some useful properties of the exponential function:
1.3.2 Big O and Little o Notation
For many applications we need a definition of the asymptotic behaviour of quantities such as functions and series; in particular we wish to find bounds on mathematical expressions and applications in computer science. To this end, we introduce the Landau symbols O and o.
Definition 1.2 (O-Notation).