MTH 481/581 Class Notes

MTH 481/581 Class Notes

Sources: (LS) Sections refer to Lin and Segel's book: Mathematics Applied to Deterministic Problems in the Natural Sciences. (BD) Sections refer to Boyce and DiPrima's book: Elementary Differential Equations and Boundary Value Problems. I also draw upon material in Strogatz's book on Dynamical Systems (ST).

  • Review Chapter 2 (1st order ODE's) and Chapter 3 (2nd order ODE's)
  • A summary review of 1st and 2nd order ODE's
  • Boundary Value Problems, BVP, and the Sturm-Liouville Problem (BD)
  • Boundary Value Problems, Solution of Non-Homogeneous BVP. (BD)
  • Orthogonal Functions (supplement)
  • Fourier Sin/Cos Series (supplement)
  • Dimensional Analysis (LS)
  • Another example of dimensional analysis: would another rower make a difference? (supplement)
  • Mathematica CDF for the Projectile with Drag Example (supplement)
  • The Art of Insight, by S. Mahalan (supplement)
  • Streetfighting Mathematics by S. Mahajan (supplement)
  • More Details on The Blast dimensional analysis, which is discussed in class and in HW2 (supplement)
  • Introduction to Systems of Linear First Order ODE's
  • Solutions of Linear Systems of ODE's
  • Notes on Regular Perturbation Methods (LS)
  • Notes on Singular Perturbation Methods (LS)
  • Dynamical Systems (BD)
  • Bifurcations and Stability (ST)

  • MATHEMATICA TOOLS:
  • Flow of a Vector Field in 2D from the Wolfram Demonstrations Project by Gosia Konwerska

  • Mathematica CDF for Dynamical Systems x' = A x. You do not need mathematica to run it. Download Wolfram Mathematical CDF PLAYER
  • Eigenvalues and Linear Phase Portraits from the Wolfram Demonstrations Project by Selwyn Hollis

  • Van der Pol Oscillator from the Wolfram Demonstrations Project by Adriano Pascoletti

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