New PDF release: Advanced mathematical methods with Maple

By Derek Richards

ISBN-10: 0521770106

ISBN-13: 9780521770101

ISBN-10: 0521779812

ISBN-13: 9780521779814

The final 5 years have obvious an important development within the use of symbolic computing and mathematical software program applications corresponding to Maple. the 1st 3 chapters of this ebook offer a common creation to computer-assisted algebra with Maple. the remainder of the booklet then develops those options and demonstrates using this expertise for deriving approximate strategies to differential equations (linear and nonlinear) and integrals. In each one case, the mathematical thoughts are comprehensively brought, with an emphasis on figuring out how recommendations behave and why numerous approximations can be utilized. the place acceptable, the textual content integrates using Maple to increase the software of conventional approximation recommendations. complex Mathematical equipment with Maple is the fitting significant other textual content for complicated undergraduate and graduate scholars of arithmetic and the actual sciences. It accommodates over a thousand routines with assorted degrees of hassle, for which recommendations are supplied on the web

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Example text

45! expÖ  45! ÒÐB  B! Ñ2  ÐC  C! Ñ2 Ó/#D! ×. 2 1 D! This object wave is a spherical wave. For the reference plane wave, we assume that the plane wave has the same initial phase as the point object at a distance of D! away from the film. Therefore, its field distribution on the film is ÐBß CÑ º l

5-5) This is a local fringe frequency that increases linearly with the spatial coordinate, B. The farther it is away from the origin of the zone, the higher the frequency will be. So, for a fixed point (local) on the hologram, we can deduce the depth information, D! ß by finding the local fringe frequency for a given wavelength of light, -! Therefore, we see that the depth information is encoded within the phase of the FZP. 19 shows the dependence of the Fresnel zone plate characteristic as a function of the depth parameter D (for D œ D!

3-12)] : <: ÐBß Cß D œ 0 Ñ œ <:! 4-2) where <:! ÐBß CÑ is now given by " ‚ >0 ÐBß CÑ. The constant, 1, in front of >0 ÐBß CÑ signifies that we have a plane wave (of unit amplitude) incident. For example, if we have an incident Gaussian beam of the profile given by expÒ  +ÐB#  C# ÑÓ, then <:! ÐBß CÑ will be given by expÒ  +ÐB#  C # ÑÓ ‚ >0 ÐBß CÑ. Let us now return to Eq. 4-2) where <:! ÐBß CÑ œ >0 ÐBß CÑ, and by using Eq. 3-12) we have <: ÐBß Cà 0 Ñ œ expÐ  45! 0 Ñ ‚ expœ 45! w w ( ( >0 ÐB ß C Ñ #1 0  45!

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Advanced mathematical methods with Maple by Derek Richards

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