MATH 5250/4250, Homework 1
Due: Thursday, 18 September 1. Find a two-term expansion in of all roots of x2 + (2 + )x + 1 + = 0 2. Find a two-term expansion in of all roots of x x2 1 + tanh( ) 3. Compute the rst two terms of all four roots of 2 x4 2x3 + x2
Math 3110 Homework 7 Due: No later than 6 December, 5pm. 1. [Holmes, 4.2 #7] Consider the eigenvalue problem d dy p (x) - r (x) y = -2 q (x) y, dx dx y (0) = y (1) = 0. (1)
Here p, q, r are given positive functions and > 0 is the eigenvalue. (a) Make a ch
Math 4/5250 Homework 6, due Tuesday, 25 Nov 1. [Holmes #6, chap. 3.3] The equation for what is known as the Rayleigh oscillator is utt 1 1 (ut )2 ut + u = 0, u(0) = 1; u (0) = 0. 3
Find the multiple-scales solution valid for large t. 2. [Holmes, #4, chap.
MATH 5250/4250, Homework 5
Due: Thursday, 13 Nov 1. Consider the system u = u - up , p > 1, - < x < . u, u 0 as |x| (a) Sketch the phase plane (u, v) of the corresponding system u = v, v = u - up . (b) Determine u(0) without computing u(x). (c) Determine
MATH 5250/4250, Homework 4
Due: Thursday, 30 October 1. [Holmes, 2.2 #1] Consider the problem uxx = a ux , u(0) = 0, u(1) = 1, 1.
(a) Find the inner and outer one-term expansion, then compute the composite expansion (b) Derive a two-term composite expansi
MATH 4220/5220, Homework 3
Due date: 23 October (Tuesday) 1. 5.1.4 2. 5.3.4, 5.3.8, 5.3.13, 3. 5.4.2, 5.4.12, 5.5.2 4. Consider a unit sphere in 3D with an initially homogeneous temperature distribution u = 1. It is then plunged into a cold bath with an o
MATH 5250/4250, Homework2
Due: Tuesday, 30 Sep. 1. The equation for the transverse displacement u = u(x) of a nonlinear beam subject to an axial load is 1 1 2 uxxxx + - u dx uxx = 0, 0 < x < 1 4 0 x with boundary conditions u = uxx = 0 at x = 0, 1. a) At