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16 Oct 2021: Γ. θ. r. θ. =. Γ. r. θ. θ. =. 1. r. Γ. ϕ. ϕ. θ. =. -. sin. θ. cos. ... θ. ϕ. =. cos. θ. sin. θ. (1.11). There are some important lessons here.

8 Jul 2021: ψ. x. (x(1)s ,y(1)s ). = b cos(x t ), (18). ... ψ. x. (x(2)s ,y(2)s ). = b cos(x t ), (20).

18 Oct 2021: The wavefunction (2.12) can be viewed as a sum of sine and cos functions and describes a complex-valued wave of wavelength. ... 2. x. The most general solution has the form. x. (. t. ). =. A. cos. (. ω. (. t. -. t.

12 Jun 2021: This too can be. resolved as. T = T cos r̂ T sin ̂. ... ei!t sin A cos. rg. lt B sin. rg. lt.

7 Apr 2021: x(t) = X R sin(!B(t t0)) and y(t) = Y R cos(!B(t t0)). ... AN=. g. 4r. 1 cos. sin(6.25). The resulting magnetic field is.

8 Jul 2021: Using spherical coordinates, wefollow ref. [12], and prescribe the tangential surface veloc-ity, us, as us = (3U0/2)(sin θ β sin θ cos θ)eθ, where U0. ... For a given value ofthe dipole strength, the maximum growth rate is obtainedfor cos k = 1, i.e.

8 Jul 2021: φ̇n = ω0 βω0 (cos χn cos χn1 ) βτ ω20 (sin χn1 sin χn ), (16). ... θ1 sin θ2 ) sin α1 sin δ cos θ1 (sin θ1 sin θ2 )]}, (46).

8 Jul 2021: Γ ={(r,θ): r = R(θ) = b cos θ. c2 b2 sin2 θ. = ... 2. ξ2+ η2. )and h = a. cosh η cos ξ ,(4.33a,b).

5 Mar 2021: Γ ={(r,θ): r = R(θ) = b cos θ. c2 b2 sin2 θ. = ... 2. ξ2+ η2. )and h = a. cosh η cos ξ ,(4.33a,b).

12 Jun 2021: We then define the usual. polar coordinates. x = r cos , y = r sin. – ... l2(4.13). with A and 0 integration constants. (You might be tempted instead to write u =. A cos B sin k/l2 with A and B as integration constants.