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Abstrak :
This survey covers a wide range of topics fundamental to calculating integrals on computer systems and discusses both the theoretical and computational aspects of numerical and symbolic methods. It includes extensive sections on one- and multidimensional integration formulas, like polynomial, number-theoretic, and pseudorandom formulas, and deals with issues concerning the construction of numerical integration algorithms.

Abstrak :
Opsi Asia dengan European style adalah opsi yang payoff-nya bergantung pada rata-rata harga aset selama masa hidup opsi dan hanya dapat dieksekusi pada saat jatuh tempo saja. Tujuan dari penulisan tugas akhir ini adalah menentukan harga opsi Asia menggunakan rata-rata geometrik dan rata-rata aritmatik melalui pendekatan terhadap rata-rata geometrik. Untuk menentukan harga opsi Asia menggunakan rata-rata geometrik dapat dilakukan dengan didekati ke kerangka Black-Scholes sehingga didapat formula Black-Scholes untuk opsi call Asia dan opsi put Asia. Sedangkan untuk menentukan harga opsi Asia menggunakan rata-rata aritmatik, dilakukan melalui pendekatan terhadap rata-rata geometrik yang dikemukakan oleh Michael Curran

Abstrak :
Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations. These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions. The text is written to facilitate easy implementation of the theory into operating numerical code. The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method. Many of these applications are useful in numerical processes of interest quite independent of differential equations. Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right. The intimate connection between collocation and Galerkin for the sinc basis is exposed via sinc-interpolation. The quadrature rules define a class of numerical integration methods that complement better known techniques, which in the case of singular integrands, often require modification. The sinc methodology of the text is illustrated on such applications as initial data recovery, heat diffusion, advective-diffusive transport, and Burgers' equation, to illustrate the numerical implementation of the theory discussed. Engineers may find sinc methods a very competitive approach to the more common boundary element or finite element methods. Further, workers in the signal processing community may find this particular approach a refreshingly different view of the use of sinc functions. Sinc approximation is a relatively new numerical technique. This book provides a much needed elementary level explanation. It has been used for graduate numerical classes at Montana State University and Texas Tech University.