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Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto

contact


Peter Philip
LMU Munich
MR ID: 639375
Reference #
OMN:202308.111371

Attributes

Posted date
2023-08-09 03:32:36
Revised date
2023-08-09 03:32:36
Level
   Undergraduate
   Graduate
Notes type
   Standard Course Offering
Topic
   Differential Equations
      Ordinary Differential Equations

Ordinary Differential Equations

Introductory course: Includes elementary solution via separation of variables and change of variables, general theory (Peano existence theorem, uniqueness of solutions, maximal solutions, continuity in initial conditions), linear ODE (existence, uniqueness, vector space of solutions, fundamental matrix solution, variation of constants, higher-order, Wronskian, constant coefficients), qualitative theory (stability at fixed points, phase portraits, Lyapunov's theorem, linearization, limit sets).

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (1.2M) 08/09/23