Download e-book for kindle: Science Matters: Achieving Scientific Literacy by Robert M. Hazen, James Trefil

By Robert M. Hazen, James Trefil

ISBN-10: 0307454584

ISBN-13: 9780307454584

Wisdom of the elemental rules and ideas of technology is key to cultural literacy. yet so much books on technology are frequently too imprecise or too really expert to do the final reader a lot good.

Science Matters is a unprecedented exception-a technology publication for the final reader that's informative adequate to be a well-liked textbook for introductory classes in highschool and faculty, and but well-written sufficient to entice basic readers uncomfortable with clinical jargon and complex arithmetic. And now, revised and extended for the 1st time in approximately twenty years, it really is updated, in order that readers can get pleasure from Hazen and Trefil's refreshingly obtainable causes of the latest advancements in technology, from particle physics to biotechnology.

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M. (z) , z-a '¥ (19) where f/J (z) is analytic near and at a. The coefficient a_I is called residue of f (z) relative to the pole a. Consider now the integral ¢ f (z) dz over a circle °whose center is at a and whose radius R is assumed to be small enough so that f/J (z) is analytic inside and on the circle. We have: f I m ¢(z~a)r f f(z) dz = a- r + f/J (z) dz . (20) a r=1 a a The last integral on the right is zero [see Eq. (12)] and the contour integrals on the right vanish unlessl r = 1. Butforr = 1, we have (putting z-a = ee j Il): 1= 2" ~f(z)dz=a_l ~~=a-l ~ ejej~d() =2nja-l.

8 = VA2 B + J32 = . 5. Symbolic Method for Solving Linear Differential Equations given by (3 B tanrp= ~=A. (44) Equation (41) can thus be written in the form 8 VA B2 [cos rp cos w t + sin rp sin w t] = VA + B2 cos (w t - rp) . (t) = 2 (45) 2 If we had identified (J,. with sin rp, (3 with cos rp, we would have obtained similar result in terms of the sine: 8 where (t) = VA2 + B2 sin (wt + rp), [1 (46) (47) We shall usually select the real part of a complex solution as the real solution and, consequently, shall always use the cosine, Eq.

3), one can be interpreted as a potential, . au. au ~x = - ax' ~y = - ay , (8) the other as the stream function, . av ~x = ay , . av ax ~y=- ~, (9) for incompressible flow. , and the quantities ~x, ~y represent the velocity components of the flow field in the x and y directions, respectively. Equations (8) and (9) show that the real part of an analytic function can always be interpreted as a potential, the imaginary part as a stream function. In the theory offunctions, the infinite plane - 00 ~ x ~ 00, - 00 ~ y ~ 00 is imaged on the surface of a sphere.

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Science Matters: Achieving Scientific Literacy by Robert M. Hazen, James Trefil

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