{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW2 - equations in Q2 Q4 Prove that 1 log(1 log(1 2...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 401 (Sec. 502) Spring, 2009 Homework 2 (due February 3) Q1. Obtain two-term expansions for the solutions of the equation (where 0 < ǫ << 1) (1 - ǫ ) z 2 - 2 z + 1 = 0 . Q2. Find the first two terms of the perturbation series solutions to the initial value problems (where 0 < ǫ << 1) (a) y - y - ǫ 1 y = 0, y (0) = 1. (b) y ′′ + 4 y + 3 y + ǫy 2 = 0, y (0) = 1 , y (0) = - 3. (c) y ′′ + ǫy - ǫ = 0, y (0) = 1 , y (0) = - 3. Q3. Determine the region of uniformity of the solutions to the differential
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equations in Q2. Q4. Prove that { 1 , log(1 + ǫ ) , log(1 + ǫ 2 ) , log(1 + ǫ 3 ) , . . . } is an asymptotic sequence as ǫ → 0. Q5. Arrange the following so that they form an asymptotic sequence as ǫ → 1 , ǫ 1 2 , ǫ 2 , log 1 ǫ , ǫ 1 2 , ǫ 2 log 1 ǫ , log(log 1 ǫ ) , ǫ 3 2 , ǫ 1 2 log 1 ǫ . ( Hint: log 1 ǫ = o ( 1 ǫ p ) as ǫ → 0 for any p > 0)...
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