5–21 Consider the following composite waveforms.
Sketch each on paper
5–21 Consider the following composite waveforms. υ1(t) = 10 [1 – e–100,000t] u(t) V υ2(t) = ...
1. (10 points) Consider the vectors u = 0 and v = | 2 [E (a) Find cosine of the angle between two vectors. Is the angle acute, obtuse, or neither? (b) Find p = projspan{v}u and verify that u-p is orthogonal to v.
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Problem 1. Consider the nonhomogeneous heat equation for u(x,t) subject to the nonhomogeneous boundary conditions and the initial condition e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution ue(a) (b) Denote v(, t)t) -)Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x,t)
Problem 1. Consider the nonhomogeneous heat equation for u(x,t) subject to the nonhomogeneous boundary conditions and the initial condition e solution u(z, t) by completing each...
please do 5 and 6
Consider the following. u = (10, -5, 0) v = (-4, 5, 0) Find u Times v. Determine if u Times v is orthogonal to both u and v by finding the values below, u middot (u Times v) = V (u Times v) = u Times v is orthogonal to both u and v. u Times v is not orthogonal to both u and v. Find a unit vector that is orthogonal to both...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t)
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...
2/2 Problem 2 Suppose that the map T: D C R2R2 (u, v) T(u, v)- (TI(u, v), T2(u, v)) defines a change of variables whose Jacobian satisfies J(T) (u, v)1 for l (u, v) E D If R C D is a region whose area is 4, then what is the area of the region T(R) T(u, v)(u, v) E R? 5 marks
2/2 Problem 2 Suppose that the map T: D C R2R2 (u, v) T(u, v)- (TI(u, v),...
HW02 9.5-9.7: Problem 5 Previous Problem Problem List Next Problem = (1 point) Consider the line L(t) Then: = (1 + 2t, 4t – 1). ? to the line is -3 – 4t, t – 2) L ? to the line is (3t – 2,4 + 6t) L ? to the line is (12t – 5, -3 – 6t) ? to the line is (4 – 4t, -8t) Note: In order to get credit for this problem all answers must...
Problem 6. Consider the function y=(2m) sin ((10/s) t+π/4). Indicate whether each of the following waveforms is equivalent to y? Briefly justify your answers. 1. (2 m) cos((10/s)1+π/4) 2. (2 m) cos((10/s) t +3r/4) 3. (2 m) cos((10/s) t-r/4) 4. (2 m) sin(10/s)t +/4+4T) 5.-(2 m) sin ((10/s)t+/4-3m) 6. (-2m) oos((10/s) t+12r/4) 7. (VZn) [cos((10/s) t) + sin((10/s)t)] 8. (2m) cos ((-10/s)t+r/4) m) 1-cos((10/s) t + π)-sin((10/s) t-π
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
1) Consider u = 2 -2), v 1 2 and w=3, where a is real number. -- a) Find the length of w. b) Find the distance between u and v. c) Find a unit vector in the direction of w. d) Find the real number a such that v and w are orthogonal. e) Find the angle 0 between u and v. remote proctor each individualsheet of paper front and