Problem 2 Show that (a2 +2)2 J B2(0) Hint: If you cannot get the desired estimate directly, try using domain decomposition.] 10 marks Problem 2 Show that (a2 +2)2 J B2(0) Hint: If you cannot get...
Problem 2 Show that e) Hint: If you cannot get the desired estimate directly, try using domain decomposition.]
There's another hint underneath it says "Recall that B2(0) is the unit disk of radius 2 in R2 " I sort of understand it but not sure where to start. Problem 2 Show that1 B2(0) Hint: If you cannot get the desired estimate directly, try using domain decomposition.] 10 marks Problem 2 Show that1 B2(0) Hint: If you cannot get the desired estimate directly, try using domain decomposition.] 10 marks
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
show its derivation to get the full mark. 2. (10 marks) 0 3 Figure 2: Mapping from input bits to different LED segments on a SSD Design a structural System Verilog module for a 7 segment display decoder that has a four bit input C, and produces a seven bit outpt Y which can be used to display the character associated with the hexadecimal value of C on a 7-segment display. The seven segments in the display are identified with...
3) (25 marks) Consider the following problem: u2(0,t) 3, u(2,t)u(2,t), t>0 u(,0) 0, 0<2 (a) Find the steady state solution u,(x) of this problem. b) Write a new PDE, boundary conditions and initial conditions for U(x, t) - u(x, t)- Cox) (c) Use separation of variables to find a solution to the PDE, boundary conditions and initial conditions. You must justify each step of your solution carefully to get full marks. (Hint: if you are unable to write the eigenvalues...
Problem 4 Let S denote the surface in R3 defined by z-(y2 + x2)-2, 1-г oo, and E be the region bounded by S and z -1. Show that you can fill E with paint but you cannot paint its surface. [10 marks] Problem 4 Let S denote the surface in R3 defined by z-(y2 + x2)-2, 1-г oo, and E be the region bounded by S and z -1. Show that you can fill E with paint but you...
Problem 1. (5 marks; 2, 3) Assume that UUniform(0,1 Answer each of the following questions. You have to show all your work to get full credit i) Find the probability density function of Y when Y = U λ (where a > 0 and λ > 0), along with the support/domain ii) Using the probability density function of Y found in part (i) and the relationship that X = log( ) complete the following three tasks: Find the probability density...
Question 4 (10 marks) When analysing the complexity of algorithms, there are three main approaches: worst case, best case and average case. As an example, consider measuring the complexity of list-merging by counting the number of comparisons used As a test example, assume the following A1: There are two ordered lists, each of length 4, say A2: Neither list contains repeats, so a! < a2 < аз < a4 and bl <b2 < b3 < b4 A3: The lists are...
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...