AME 60611 Exam 1

[goodwine]

Instructions:

1. This exam must be completed and submitted to the instructor by 5:00 pm, Wednesday, October 11.
2. You may only consult your course notes, the course text, any book that is listed on the reference list on the course syllabus, any handouts on the course web page (homework solutions) and the instructor. If you require an integral table, you may use one from any reference; however, you may only consult the integral table from that reference if it is not on the course reference list. You may not discuss the exam with any other person or refer to any other notes or references until after the final due date.
3. You may use computer programs such as Mathematica, Matlab, Maple, etc. or your calculator to make any plots, check algebraic computations or to check any answers. To receive credit for a problem, you must submit the work supporting the answer to the problem.
4. The time limit for the exam is six hours. If you exceed that time, clearly indicate on your work what was completed in the six hours and what was completed after the time limit. You may not split the time into segments, e.g., you may not work on the exam three hours, take a break, and then work on it for three more hours later.
5. When you complete the exam, submit it to the instructor as soon as is practically possible. If he is not in his office, put it under his door or in his mailbox in the AME office.
6. Referring to any material other than what is allowed, exceeding the time limit, communicating with any person other than the instructor regarding the exam or any other actions inconsistent with the rules outlined above is a violation of the department and University policy of academic integrity and will result in a failing grade for the course.

Problems:
Unless otherwise indicated, the problems are from the course text. Each problem is worth 25 points.

1. Chapter 1, number 6
2. First order equations:
   1. Find the solution to
      • 
   2. Show that if
      • 
      where R depends only on the quantity xy then the differential equation
      • 
      has an integrating factor of the form
      • 
      Find a general formula for this integrating factor.
3. Chapter 3, number 12.
4. The equation for the relativistic perturbation of a planetary orbit is
   • 
   Use an expansion of the form
   • 
   to determine an approximate solution up through first order in the perturbation parameter. Identify the secular term in the first order term and use strained coordinates to eliminate it.