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- Question : EX1 - Show that if F = 0 and
- Question : EX2 - Find the equilibrium (time independent) velocity, density, and pressure distributions for a gas satisfying (1.13) with
- Question : EX3 - Let F(x, t)
- Question : EX4 - If F(x, /) = 0, u(x, 0) = 0, p(x, 0) = p0 +
- Question : EX1 - If f(x) is defined for 0 x 1 by /(x) = eJ' sin ttx and for other values by the extension /( - x ) = - /( x ) , / ( 2 - x ) = - / ( x ) , find (a) /(3/2), <b> 4 - ^ j , (c)/(14).\" 1 The One-Dimensional Wave Equation,,The One-Dimensional Wave Equation,18580281,Problem EX2, Show that if g(x) satisfies (2.14) and (2.15)
- Question : EX2
- Question : EX3 - A string of length / = 1 is initially fixed in the position u = sin-n-x, and is released at time t
- Question : EX4 - (a) Find
- Question : EX5 - (a) Show that the solution (2.16) is an odd periodic function of period 21 in x. (b) Show that the solution (2.16) is periodic of period 2l/c in t; that is, that / 2l\ ul X, t +
- Question : EX6 - Show that the solution (2.16) satisfies u(^l
- Question : EX7 - Find the generalized solution corresponding to the initial data f(x ) = 0, 0 for 0
- Question : EX8 - Derive the solution of the initial-boundary value problem d2u 2d2u n dr dx2
- Question : EX9 - Derive the solution of the initial-boundary value problem d2u _ 2d2u A c *
- Question : EX10 - Derive the solution of the problem d2u 2d2u A r . = 0 f o r o < x < i, t > x,
- Question : EX11 - A rod of uniform elastic material of length | li
- Question : EX1 - Show that if du/dx has a discontinuity at a point (x, 7), then this discontinuity is propagated along at least one of the characteristics through (x, 7).
- Question : EX2 - . Show that a discontinuity in d2u/dx2 is also propagated along at least one characteristic through (x, 7).
- Question : EX3 - Suppose that du . 1 du dX C dt has a jump discontinuity of magnitude one across a characteristic x + ct = x0 (that is, a
- Question : EX4 - It is easily verified that for any function/(x) that is twice continuously differentiable and any function g(x) that is continuously differentiable for
- Question : EX1 - Find
- Question : EX2 - Find
- Question : EX3 - Find the domain of influence of a point (x0, 0) when d
- Question : EX4 - Solve Exercise 11 of Section 2 when the right end x
- Question : EX5 - Show that if /(x) is even about x
- Question : EX6 - Show that if du/dx ~ 0 at x = 0 and x = /, the solution u satisfies the recursion relations u(x, t + =
- Question : EX7 - Show that if du/dx
- Question : EX8 - If/(x ) = x2 (l
- Question : EX9 - If/(x ) = (1
- Question : EX10 - Sketch the x-t diagram of the solution of the problem where m(0, t) = du/dx(I, t) = 0, /(x) = 0, and g(x) = 0 except in a small neighborhood of x
- Question : EX1 - Find the value at x = f , t
- Question : EX2 - If d2U _ d2U _ dt2 dx2 ~ e u(x, 0) = 0 0) = 0 ^ ( 0 , 0 = 0 , dx ^ ( i , 0 = 0 , dx for 0 < x < 1, for 0 jr 1, for 0 jc 1,
- Question : EX3 - Find the solution of d2U _ dt2 d2U
- Question : EX4 - If Qj I 1 S Qj Qj o 7 -- * O -u II ' Il IIII o 1 1 |I|I II * P " o I 0 ^ 0 0^ o o o IA IA A IA IA A V p find u(i, I).
- Question : EX5 - If d2U d2U < r i . n d f - d ^ = l ~ x fo r 0 < ? : < 1
- Question : EX6 - Show that if the force function F in (5.3) is a function of x only, the solution u is periodic in t of period 2//c. That is, / 2l\ zd x, t +

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