Advanced Engineering Math 9th Edition with Mathematica by Erwin Kreyszig

By Erwin Kreyszig

Booklet by way of Kreyszig, Erwin

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13 help in obtaining the right answer (linear dependence). 10. Yes. The relation cos2 x ϩ sin2 x ϭ 1 is irrelevant here. 12. Yes. Consider the quotient. 14. No. Once and for all, we have linear dependence of two (or more) functions if one of them is identically 0. This problem is important. dyЈ dy dz dyЈ 16. y Љ ϭ ᎏ ϭ ᎏ ᎏ ϭ ᎏ z dy dx dy dx 18. zЈ ϭ 1 ϩ z 2, dz/(1 ϩ z 2) ϭ dx, arctan z ϭ x ϩ c1, z ϭ tan (x ϩ c1), y ϭ Ϫln ͉cos (x ϩ c1)͉ ϩ c2 This is an obvious use of problems from Chap. 1 in setting up problems for this section.

Mathematically, we go from a homogeneous to a nonhomogeneous ODE, which we solve by undetermined coefficients. qxd 9/21/05 10:57 AM Page 49 Instructor’s Manual 49 New Features Resonance (11) y ϭ At sin ␻0 t in the undamped case Beats (12) y ϭ B(cos ␻t Ϫ cos ␻0 t) if input frequency is close to natural Large amplitude if (15*) ␻2 ϭ ␻02 Ϫ c 2/(2m2) (Fig. 8, page 90 2. 5t. 5t), and the student should perhaps be reminded that this is not resonance, of course. 4. 25 cos t. Note that yh ϭ e؊2t(A cos t ϩ B sin t); of course, this is not resonance.

5. Euler–Cauchy Equations, page 69 Purpose. Algebraic solution of the Euler–Cauchy equation, which appears in certain applications (see our Example 4) and which we shall need again in Sec. 4 as the simplest equation to which the Frobenius method applies. We have three cases; this is similar to the situation for constant-coefficient equations, to which the Euler–Cauchy equation can be transformed (Team Project 16); however, this fact is of theoretical rather than of practical interest. Comment on Footnote 4 Euler worked in St.

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