{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math4250exam1_2012

math4250exam1_2012 - Spring 2012 Math 4250/6250 Exam#1 This...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Spring 2012 Math 4250/6250 Exam #1 This take-home exam covers the material on curves (class notes #1 through #6 and DoCarmo Chapter #1). Undergraduates must pick four questions and may substitute one or more graduate exam problems for undergraduate exam problems for bonus credit. Graduate students must pick one undergraduate problem and two graduate problems and may do all three graduate problems for bonus credit. You are permitted to use You are not permitted to use Maple (or Mathematica or MATLAB) The internet A calculator (or graphing calculator) DoCarmo Other books Your notes Other people’s notes Your brain Other people’s brains Class notes posted on the website Undergraduate Exam Problems 1. Find the (unsigned) curvature κ ( t ) of the parametrized plane curve given below in polar coor- dinates: - 2 2 4 6 - 4 - 2 2 4 α ( t ) = ( r ( t ) , θ ( t )) = (4 cos 3 t + 2 , t ) 2. Find the curvature and torsion of the curve given by α ( t ) = (1 + cos t, sin t, 2 sin t 2 ) . 3. We learned to write the set of lines in the plane using the coordinates ( θ, p ) where ( θ, p ) is the line which satisfies the equation: (cos θ ) x + (sin θ ) y = p, Suppose that α ( s ) = ( α 1 ( s ) , α 2 ( s )) is an arclength-parametrized plane curve, and that ( s )
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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