EGM 6321-ADVANCED ORDINARY DIFFERENTIAL EQUATIONS
 
Offered Spring Semester                                                                          Instructor: Dr.U.H.Kurzweg

Lecture                  Topic                                            Lecture                     Topic


    1.      Introductory Remarks                                                  SECOND HOUR EXAM
    2.      Solution of 1ST Order ODEs                            31.      Phase Plane Methods
    3.      Orthogonal Trajectories                                    32.      Solution Near Critical Points
    4.      2nd Order ODEs, Abel Identity                        33.      Stability Criteria.
    5.      Solution by Taylor Series                                  34.      Van der Pol Equation
    6.      Airy and Hermite Equations                              35.      Bogliuboff-Kryloff Method
    7.      Fuch's Theorem, Laurent Expansion                  36.      Duffing Equation
    8.      Frobenius Technique                                         37.      Poincare-Linstedt Expansion
    9.      Bessel Equation and Functions                          38.      Harmonics and SubHarmonics
  10.      Hyperbolic Bessel Equation                               39.      Blasius Equation
  11.      Generalized Bessel Equation                              40.      Thomas Fermi & Emden Equations
  12.      Hypergeometric Equation                                  41.      Weighted Residuals
  13.      Singular Point at Infinity
  14.      Legendre Eq., Rodrigues Formula                                THIRD HOUR EXAM
  15.      Chebyshev Equation and Polynomials
  16.      Mathieu and Hills Equations
  17.      Asymptotic Expansions

             FIRST HOUR EXAM

  18.     Integral Representations                                       No required Text. Collateral reading:
  19.     Laplace Kernel                                                    Ince,"Advanced Differential Equations"'
  20.     Integral Representaion of J[n,x]                            Davis,"Intro to Linear and Non-Linear Diff.
  21.     Integrals for Hermite and Laguerre Polyn.             and Int. Equations"
  22.     Euler Kernel         
  23.     Legendre Polynomials via Euler Kernel
  24.     Laplace Method                                                  Grade Determination:
  25.     Stationary Phase Method                                     Weekly HW-25%, 3 In-Class Exams-25% each
  26.     Saddle Point Technique                                        No Final Exam
  27.     JWB Method
  28.     Non-Linear 2nd Order ODEs
  29.     Elliptic Integrals
  30.     Ellipticfunctions