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Elementary Functions of Complex Variables

In the course of analysis, elementary functions of the complex variable s arise, such as exp(-s), sin Vs, log(s), and so forth. We must carefully define these operations so that in the limit w - 0, these operations reduce to conventional operations on real variables. We begin our study on the most elementary function, the power law relationship [Pg.334]

We next combine this result with properties of the exp is), which can be proved to have the usual power series representation [Pg.334]


John continued to overestimate my mathematical skills by persuading me to take an extension course with him. It was enticingly listed as Functions of a Complex Variable and required the purchase of a textbook entitled Conformal Mapping. The syllabus warned that students should not undertake this course without having worked through three years of calculus - John convinced me that in my case one semester of elementary calculus, more than a decade ago, would suffice. [Pg.154]

The definition of many elementary functions can be extended to complex variables. Pol5momial, exponential, and logarithmic functions are discussed here. [Pg.17]

The formal solution to the problem of describing the unsteady-state concentration distribution in a soil column has now been completed. Equation [21] can be used directly for computations using computers that have the software to evaluate the real and complex parts of a complex function such as 7 3/2,t. If such software is not available the real and imaginary parts of 7 3/21 are presented in Appendix 2, in terms of elementary functions that do not involve complex variables, as Eq. [A24] and [A25], respectively. [Pg.175]

The speed of a heterogeneous reaction (or its rate) is usually an extremely complex function that depends on physico-chemical and textural variables (shapes and phase dimensions). (Jenerally, the volumetric or areal speed cannot be defined. Despite thus, a certain nrrmber of heterogeneorrs reactions follow the law , which means that the rate can be written as a product of two functions as in the case of the elementary steps ... [Pg.110]


See other pages where Elementary Functions of Complex Variables is mentioned: [Pg.17]    [Pg.17]    [Pg.19]    [Pg.21]    [Pg.23]    [Pg.334]    [Pg.17]    [Pg.17]    [Pg.19]    [Pg.21]    [Pg.23]    [Pg.334]    [Pg.247]    [Pg.333]    [Pg.230]    [Pg.65]    [Pg.176]    [Pg.183]    [Pg.48]    [Pg.289]    [Pg.350]    [Pg.144]    [Pg.191]    [Pg.210]    [Pg.239]    [Pg.129]    [Pg.106]   


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