PHYS 598 hw0 - Revision and Warm-up exercises These...

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

View Full Document Right Arrow Icon
Physics 498/MMA Handout 0 Fall 2007 Mathematical Methods in Physics I m-stone5 Prof. M. Stone 2117 ESB University of Illinois Revision and Warm-up exercises These problems are designed to exercise your basic mathematical skills. They are not de- signed to be easy! Each one has some twist that is designed to catch you out if you merely manipulate symbols without thinking. Differential Calculus : After taking a previous version of this course, a student claimed that the expression y ( x ) = sin ω ( x - L ) ω sin ωL Z x 0 f ( t ) sin ωt dt + sin ωx ω sin ωL Z L x f ( t ) sin ω ( t - L ) dt is the solution to the problem: “Find y ( x ) obeying the differential equation d 2 y dx 2 + ω 2 y = f ( x ) on the interval [0 , L ] and satisfying the boundary conditions y (0) = 0 = y ( L ).” First examine her solution to see if it obeys the boundary conditions. Then, by differentiating her solution twice with respect to x and substituting the result into the differential equation, check to see if her solution obeys it.
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