By William J. Thompson
Subject matters are divided among evaluation fabric at the arithmetic history; numerical-analysis tools reminiscent of differentiation, integration, the answer of differential equations from engineering, lifestyles and actual sciences; data-analysis functions together with least-squares becoming, splines and Fourier expansions. targeted in its venture orientation, it encompasses a monstrous volume of routines with emphasis on life like examples from present functions.
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Extra info for Computing for Scientists and Engineers, a workbook of analysis, numerics, and applications
In Chapters 9 and 10 on Fourier expansions we make detailed study of phenomena described in terms of x or in terms of the complementary variable k, or in terms oft and its complementary variable Clear expositions of the relations between complex exponentials and vibrations are given in detail with many applications in Pippard’s omnibus book. Vibrations and waves are described very completely at an introductory level in the book by Ingard. 5 DIVERSION: INTERPRETING COMPLEX NUMBERS The development of the interpretation of complex numbers provides an example of the consequences of education and of the dominance of scientific thought by mathematical representations.
Many quantities derived from wave functions, such as scattering amplitudes, are also intrinsically complex-valued. This leads to the scientific use of “analytic continuation,” a concept and technique familiar in mathematics but of more recent use in the natural sciences. 4 the circular functions and the hyperbolic functions, respectively. In terms of complex variables, however, these hyperbolic functions are essentially just the circular functions evaluated for purely imaginary arguments, or vice versa.
Vibrations and waves are described very completely at an introductory level in the book by Ingard. 5 DIVERSION: INTERPRETING COMPLEX NUMBERS The development of the interpretation of complex numbers provides an example of the consequences of education and of the dominance of scientific thought by mathematical representations. Since many scientists claim that a phenomenon is not understood until it can be described mathematically, it is interesting to discuss the relation between “the queen and servant of science” and the natural sciences.