New PDF release: Computing for Scientists and Engineers, a workbook of

By William J. Thompson

ISBN-10: 0471547182

ISBN-13: 9780471547181

Themes are divided among assessment fabric at the arithmetic heritage; numerical-analysis tools resembling differentiation, integration, the answer of differential equations from engineering, existence and actual sciences; data-analysis purposes together with least-squares becoming, splines and Fourier expansions. precise in its undertaking orientation, it incorporates a huge volume of workouts with emphasis on sensible examples from present functions.

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Additional info for Computing for Scientists and Engineers, a workbook of analysis, numerics, and applications

Sample text

11, explain why the cosine and sine functions are called “circular” functions. 54) valid for any complex-valued u. n These two equations may be used to provide a general rule relating signs in identities for hyperbolic functions to identities for circular functions: An algebraic identity for hyperbolic functions is the same as that for circular functions, except that in the former the product (or implied product) of two sinh functions has the opposite sign to that for two sin functions. 15 Provide a brief general proof of the hyperbolic-circular rule stated above.

30) can be generalized to the product of n complex numbers, as the following exercise suggests. 32) which is called De Moivre’s theorem. n This remarkable theorem can also be proved directly by using induction on n. Reciprocation of a complex number is readily performed in polar-coordinate form, and therefore so is division, as you may wish to show. 34) where it is assumed that r2 is not zero, that is, z2 is not zero. 10). 2 that complex-number multiplication and division in Cartesian form are much slower than such operations with real numbers, these operations may be somewhat speedier in polar form, especially if several numbers are to be multiplied.

N This remarkable theorem can also be proved directly by using induction on n. Reciprocation of a complex number is readily performed in polar-coordinate form, and therefore so is division, as you may wish to show. 34) where it is assumed that r2 is not zero, that is, z2 is not zero. 10). 2 that complex-number multiplication and division in Cartesian form are much slower than such operations with real numbers, these operations may be somewhat speedier in polar form, especially if several numbers are to be multiplied.

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Computing for Scientists and Engineers, a workbook of analysis, numerics, and applications by William J. Thompson


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