Get A Guided Tour of Mathematical Methods: For the Physical PDF

By Snieder R.

ISBN-10: 0521542618

ISBN-13: 9780521542616

ISBN-10: 0521834929

ISBN-13: 9780521834926

Unlike conventional textbooks for college students and pros within the actual sciences, this booklet offers its fabric within the type of difficulties. the second one variation comprises new chapters on dimensional research, variational calculus, and the asymptotic assessment of integrals. The booklet can be utilized by way of undergraduates and lower-level graduate scholars. it might function a stand-alone textual content, or as a resource of difficulties and examples to counterpoint different textbooks. First variation Hb (2001): 0-521-78241-4 First version Pb (2001): 0-521-78751-3

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Extra resources for A Guided Tour of Mathematical Methods: For the Physical Sciences

Example text

The notation of the strength of left- and right-going waves is indicated. 28 Power series coefficient of the combined stack is the product of the transmission coefficient of the individual stacks: ? T = TL T R . 32) However, this result is wrong and we will discover why this is so. 4 again. The unknown quantities are R, T , and the coefficients A and B for the right-going and left-going waves between the stacks. An incident wave with strength 1 impinges on the stack from the left. Let us first determine the coefficient A of the right-going waves between the stacks.

Perpendicular to the surface f = const. Now that we know this, the gradient can still point in two directions because one can move in two directions perpendicular to a surface. 3 where we consider a step δr in an arbitrary direction. 10) where θ is the angle between ∇ f and δr. The change δ f is largest when the vectors ∇ f and δr point in the same direction because in that case cos θ is equal to its maximum value of 1, that is when θ = 0. We also know that δ f increases most rapidly when δr is directed in such a way that one moves from smaller values of f towards larger values of f .

The velocity v of the air can be expressed in spherical coordinates as: ˆ. 20) The motion of the air is governed by Newton’s law, but when the velocity v and the force F are both expressed in spherical coordinates it would be wrong to express the θ-component of Newton’s law as: ρdvθ /dt = Fθ . The reason is that the basis vectors of the spherical coordinate system depend on the position. When a particle moves, the directions of the basis vectors change as well. This is a different way of saying that the spherical coordinate system is not a Cartesian system where the orientation of the coordinate axes is independent of the position.

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A Guided Tour of Mathematical Methods: For the Physical Sciences by Snieder R.

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