Mathematics 131 - Elementary Differential Equations

Spring Semester 2005

Text

Differential Equations and Boundary Value Problems, Third Edition, by C. Henry Edwards and David E. Penney, Pearson Education, Inc., Prentice-Hall, Upper Saddle River, NJ.

Instructor

William K. Allard, Professor of Mathematics
  • Office: 024A Physics Building
  • Phone: (919) 660-2861
  • Fax: (919) 660-2821
  • E-mail: wka@math.duke.edu
  • Office Hours: Tuesday and Thursday, 1:00-3:00 pm, and by appointment.
  • Time and Place for Mathematics 131, Spring Semester 2005

  • Tuesday and Thursday, 11:40am-12.55pm, Physics 216
  • Syllabus For Mathematics 131

    We will cover the material corresponding to the homework problems; this is, roughly, Chapters 1-6 and 9 in the text.

    Grading

    There will be two in-class exams, a weekly quiz, and a final exam; these will count 40%, 20% and 40% of your grade, respectively. It is very likely, though, that there will be some computer projects that will make up a significant part of your grade; I don't want to be more specific at this point in time because I want to see how well these projects work out. The homework assignments will graded and returned to you; I will keep track of the homework grades but they will not count toward your grade for the course.

    Students with excused absences will be given a make-up exam. No quizzes or homework will be made up for credit, but it's important to make it up for your own benefit. Late homework will not be accepted.

  • Answer key for Test One. Problems 1-5 counted 10 points each and problems 6-7 counted 20 points each.
  • Answer key for Test Two.

  • Comments

    What follows was written by Prof. David Kraines and modified ever so slightly by me. Differential equations arise from the study of problems in virtually every area of science and engineering as well as in many social science fields. In this course, you will study how to construct mathematical models of real world phenomena and how to use analytical, numerical and graphical techniques to explore these models. Although you will be expected to find explicit solutions to some differential equations, the course will emphasize the qualitative meaning of the solution. You will be expected to use computer software to find numerical estimates of solutions and to graph and interpret solution curves (trajectories). No programming experience is required.

    The textbook website has several differential equations demos and illustrations of some of the examples and exercises from the text. Pull down the "jump to" menu to access the solution manual and to download Maple Worksheets. The ODE solver at this site may be quite useful in some assignments. I suggest you download dfield7 and pplane7; these programs must be run under Matlab.

    To gain a solid grasp of differential equations, it is essential for you to solve many exercises. Make an effort to understand how to complete the "practice" problems. Detailed solutions to most of the odd numbered exercises are given in the on-line solution manual. All answers to the problems that you are to turn in must be appropriately justified for full credit. Some of the assigned exercises are quite challenging even when the answer is in the back of the book.

    Constructive cooperation, in the sense of exchanging ideas about the exercises, is encouraged for the assigned problems; you must, however, acknowledge any help you receive. Copying solutions from others or allowing others to copy from you will be considered a violation of the Honor Code.

    You will use a computer algebra system such as Maple, Matlab, or Mathematica, for many of the assignments. To download Maple or other software to your own computer, consult the OIT software website. As far as I know you can't download Matlab; you can run it remotely on many machines on campus. Other specialized differential equations software is available on the web.

    Computer projects, found at the end of several of the sections, will be assigned from time to time. The first few computing assignments and some of the later ones will be team projects. I will attempt to pair those who are more comfortable with mathematical computer software with those who are less so.

    Math 131 Notes

  • Existence and uniqueness for ordinary differential equations. PDF
  • An example of nonuniqueness and an application of the uniqueness theorem to separable equations. PDF
  • A formula for the solution of the general first order linear differential equation. PDF
  • Solution of the hailstone problem, number 42 on page 55. PDF
  • Time to blowup. PDF
  • A maple program for Euler's method. Text file
  • A maple worksheet for Euler's method. Maple Worksheet
  • A maple program for the improved Euler's method. Text file
  • A maple worksheet for the improved Euler's method. Maple Worksheet
  • Variation of constants. PDF
  • Kepler's laws of planetary motion. PDF
  • The computer assignment. PDF
  • A nifty example. PDF
  • Fourier series. PDF
  • The vibrating string. PDF
  • A final exam take home problem. PDF
  • A second final exam take home problem. PDF
  • Stability, Part One. PDF
  • Homework for Math 131, Spring Semester 2005

    Homework.

    Some References

    Coming later!

    The Duke Community Standard

    "Duke University is a community of scholars and learners, committed to the principles of honesty, trustworthiness, fairness, and respect for others. Students share with faculty and staff the responsibility for promoting a climate of integrity. As citizens of this community, students are expected to adhere to these fundamental values at all times, in both their academic and nonacademic endeavors."

    Specifically,

  • All quizzes and exams will be done without books or notes and without collaborating with any other student.
  • Homework assignments can discussed with other students in the course and I encourage you to do so. However, solutions must be written up individually without consulting anyone else's written solution and any assistance received must be acknowledged.
  • Calculators may be used on homework but not on quizzes or exams unless specified in class in advance.
  • Return to: Duke University * Mathematics Department
    wka@math.duke.edu
    Last modified: January 12, 2004