1. [10 marks] Consider the quadratic equation x2-0.03x 3.99. a) Write this as a perturbation prob...
Please show all steps for how to solve this perturbation problem. Thank you. 1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation problem. Is it singular or regular? (b) Letting x = ao + aie+ a2e2 + . . . solve up to and including terms of order 0(e2). (c) Compare the solution with the "exact" solution. 1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation...
Can someone help show how to answer this question. Thanks in advance. 3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e) 3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
3. [8 marks] Consider the differential equation Solve the regular perturbation problem with error of order 0(e), ie. up to and including terms of 0(e) 3. [8 marks] Consider the differential equation Solve the regular perturbation problem with error of order 0(e), ie. up to and including terms of 0(e)
3. [8 marks] Consider the differential equation Solve the regular perturbation problem with error of order 0(e), ie. up to and including terms of 0(e)
Consider a one-dimensional (1D) harmonic oscillator problem, where the perturbation V causes a modification of the oscillator frequency: 2 K22 H = H. +V, (1) 2 K2 V = - K +K > 0. Of course, this problem (1), (2) is trivially solved exactly yielding the oscillator solutions with a new frequency. Show that corrections to the nth energy level as calculated within the perturbation theory indeed reproduce the exact result, restricting yourselves to terms up to the second order...
2. (10 points) Given a quadratic equation x2 + bx + c = 0, write a paragraph which details the method for completing the square.
You are given that there exists a solution to the equation et = 4 sin (2) in the interval [0, 0.5]. a) Use the iterative method explained during the course to find this solution up to 3 decimal places. Make sure you include enough details of the calculation and that your cal- culator is set in radians for this problem. [3 marks] b) Now estimate the same solution using the Maclaurin expansion of the function f(x) = e" – 4...
Exercise 8: Time dependence of a two-level system Consider a two-level system with stationary states a and b with unperturbed energies and E() and corresponding eigenfunctions ф ) and 4°, respectively. Assume E ) > E 0. such that the Bohr angular frequency wi(EEis positive. A time-independent perturbation V is switched on at time t 0 a) Write down the coupled set of equations for the coefficients ca(t) and c(t) of the wave function of the system: Note that we...
Q3. [22 marks] The Dirichlet's problem for a disc of radius a is stated as follows: r(a, θ)-/(0) for osas2m, where the function f (0) is integrable [10 marks] Find the general solution of u(r, θ) (i) (7 marks] if f (θ)-sin|-θ | , find the specific solution u (r,0) (ii) [ (ii) [5 marks] Use the solution in (ii) to deduce that 4n1-9) 18 Q4. [24marks] Consider the second order linear partial differential equation Q3. [22 marks] The Dirichlet's...
NOTE: h=(b - a) / N Consider the differential equation y" y' +2y + cos(), for 0 x , with boundary conditions (0) 0.3, Show that the exact solution is (x)(sin3 cos())/10. (a). Consider a uniform grid with h (b? a)/N. Set up the finite difference method for the problem. Write out this tri-diagonal system of linear equations for yi, (b). Write a Matlab program that computes the approximate solution yi. You may either use the Matlab solver to solve...