Prove that the functions (a)
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Numerical Analysis
- 3. Verify that u(r,l) = sin(x – at) satisfies the wave equation:arrow_forwardShow that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.arrow_forwardConsider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)).Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equationarrow_forward
- 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) - v sin(e) and yusin(0) + v cos(0).arrow_forwardVerify that the function u(x, t) = (r – at)° + (x + at)° satisfies the wave equation uu =arrow_forward11) Calculate the Jacobian, J, for the change of variables x = u cos(e) - v sin(e) and y = u sin(0) + v cos(0).arrow_forward
- 2. Suppose that a motion described by the vector valued function (i.e. position function) r(t) has velocity given by r'(t) = v(t) = (5 cos t, 5 sin t, –2) and that r(0.) = (2,1, 1). Find the formula for the position function r(t).arrow_forward- 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) + v cos(0).arrow_forward(a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t I U (x, 0) = 0. (b) Solve the inhomogeneous wave equation on the real line Utt- c²Uzz = sinx, x ER ᏆᏆ U(x, 0) = 0, U₁(x, 0) = 0. Explain what theory you are using and show your full computations.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage