Midterm2practice - y x = e x g x To further simplify things...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
NAME: Math 385 — Midterm 2 practice Total points: 100 . Please explain all answers. Calculators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know. You can get partial credit for it. 1. [25 points] Calculate (so don’t give me a memorized answer for) the Fouries series expansion for f ( t ) = 2 + t in - 2 t 2. (Note that f ( t ) - 2 is an odd function.) 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
NAME: 2. [25 points] Find all eigenvalues and associated eigenfunctions for the following boundary value problem for y ( x ): y - 2 y + λy = 0 y (0) = y (2) = 0 You may want to consider the substitution
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y ( x ) = e x g ( x ). To further simplify things you may also want to define μ = λ plus (or minus) an ap-propriate constant. (But your final answer has to be in terms of y ( x ) and λ ) 2 NAME: 3. [25 points] Find the general solution of this forced mechanical oscillator. What will happen to the solution as t → + ∞ ? Does this result depends on initial conditions and why? x 00 + 2 x + 7 x = 2 sin (3 t ) 3 NAME: 4. [25 points] Find the general solution of the following ODE for y ( x ): y 00-6 y + 8 y = 8 x 2 + 1 4...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern