Titlebook: Analysis for Computer Scientists; Foundations, Methods Michael Oberguggenberger,Alexander Ostermann Textbook 20111st edition Springer-Verla

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Antiderivatives,. Conversely, the question about the reconstruction of a function . from its local rate of change . leads to the notion of . which comprises the totality of all functions that have . as their derivative, the . of .. Chapter 10 addresses this notion, its properties, some basic examples and applicatio

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Definite Integrals,ons of the form .(.)Δ. and taking limits. Such sums appear in many applications including the calculation of areas, surface areas and volumes as well as the calculation of lengths of curves. This chapter employs the notion of Riemann integrals as the basic concept of definite integration. Riemann’s

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Taylor Series,on we discuss the approximation of a function by Taylor polynomials and by Taylor series in this chapter. As important applications we will use Taylor series to compute limits of functions and to analyse various approximation formulae.

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Numerical Integration,e integrand . and computes from that the value of the integral. In ., however, it is difficult and often even impossible to find an antiderivative . as a combination of . functions. Apart from that, antiderivatives can also be fairly complex, as the example ∫..sin . d. shows. Finally, in concrete ap

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Integration of Functions of Two Variables,ntegral calculus to functions of two variables. This arises, for example, if one wants to find the volume of a solid that lies between a domain . in the (.,.)-plane and the graph of a non-negative function .=.(.,.). In this section we extend the notion of Riemann integrals from Chap. . to double int

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Linear Regression, importance of influencing factors, and prediction, in all areas of human, natural and economic sciences. Computer scientists who work closely with people from these areas will definitely come across regression models..The aim of this chapter is a first introduction into the subject. We deduce the c

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Differential Equations,ems will be discussed in the next chapter..After presenting the general definition of a differential equation and the geometric significance of its direction field, we start with a detailed discussion of first- order linear equations. As important applications we discuss the modelling of growth and