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Math 386 Neumann eigenvalue problem
In class we mentioned the following exercise: nd all eigenvalues R and eigenfunctions y(x) for the eigenvalue problem y + y = 0, 0 < x < ,
with the Neumann boundary conditions y (0) = 0, y () = 0. Solution. First consid
Project II Numerical Methods
March 5, 2010
The purpose of this project is to give you a deeper understanding of
numerical methods. It assumes that you have worked through the rst Iode
project as well as the lab guide on numerical methods.
Math 386 Homework #12
Due Wednesday 2 May, 5:00pm Section 9.5 #3, 9. Be sure to explain where your answers come from. Problem A: Solve the heat equation with Neumann boundary conditions: ut = 3uxx , ux (0, t) = ux (2, t) = 0, x 4x u(x, 0) = 1 + cos + 7 co
Project I Direction Fields
Richard S. Laugesen
Goal of the project
Consider the dierential equation dy = f (x, y). dx We aim to understand graphically how properties of the function f (x, y) aect the direction eld. In particular, we consider functions f t
Math 386 Spring 2007 Quiz 4 Solutions
Use the method of Eigenvector Decomposition to nd a particular solution of the nonhomogeneous system x y = 2 1 4 2 x 1 + 4t . y e
You may use that the eigenvalues, eigenvectors are 1 = 0, v1 = 1 , 2 2 = 4, v2 = 1 . 2
Math 386 Spring 2007 Homework 10
The rst four questions build upon the Section 3.8 material and Orthogonality Supplement covered in class. A. Find all eigenvalues R and eigenfunctions y(x) for the eigenvalue problem y + y = 0, 0<x< , 2 with the mixed boun
Math 285 Spring 2003 Test 2 Solutions
Total points: 100. Do all questions. Explain all answers. No notes, books, calculators or computers. 1. [6 points] For the following dierential equation, write down the form of the complementary solution yc , and of t
Math 386 Spring 2007 ~ Quiz 2 Solution
Do #1 or #2, but not both.
1. Solve the differential equation m2y + 2333; = 5y3.
Answer: y = 1/x/2zr1 + 0x4.
The equation has Bernoulli form (since it has a 1/ term, a y term, and a
power of y). The pow
Math 386 Fall 2007 - Quiz 3 Solutions
Consider a forced system x + 1 x + 25x = cos(t). 10
(a) [0.75 points] Compute a steady periodic (particular) solution. Solution. Undetermined Coefficients Rule 1 tells us to try xp = A cos t + B sin t. We do not need
HOMEWORK 1 SUPPLEMENT ALGEBRA, CALCULUS REVIEW A little time spent now reviewing algebra and calculus facts will save you a lot of time later. So pull your calculus textbook o the bookshelf and do the following questions. 1 (1) Suppose y = x + C. True or