Tentative Class Schedule:
Lecture 1: Introduction to AMS501. ODE's; definitions and
examples; IVP and BVP.
Lecture 2: Theory of homogeneous linear equations; Wronskian,
and ill-posed problems. Constant coefficient equations.
Lecture 3: Linear homogeneous and inhomogeneous equations. Methods
variation of parameters and undetermined coefficients.
Lecture 4: The method of Green's function.
Lecture 5: Eigenvalue problems; Sturm-Liouville problem.
Lecture 6: First order nonlinear ODE's. Introduction into
Lecture 7: Systems of linear differential equations. Systems with
constant coefficients and non-defective matrices.
Lecture 8: Systems of linear differential equations with
non-diagonalizable matrices. Nonhomogeneous systems of linear
Lecture 9: Examples of mathematical modeling. Transformation to
dependent and independent
Lecture 10: Equations of Lagrangian and Hamiltonian mechanics.
Lecture 11: Review of methods for exactly solvable equations.
Mar. 4: Midterm Exam (in class)
Lecture 12: Review of the midterm exam. Classification of singular
of homogeneous equations.
Lecture 13: Local behavior near ordinary points. Local series
about regular singular points.
Lecture 14: Frobenius series for equations with regular singular
Lecture 15: Local behavior at irregular singular points of
linear equations. The method of dominant balance.
Lecture 16: Irregular singular point at infinity.
Lecture 17: Local analysis of inhomogeneous linear equations
Lecture 18: Asymptotic analysis of nonlinear equations. Spontaneous
Lecture 19: Nonlinear autonomous systems. Classification of critical
Lecture 20: Critical point analysis of two-dimensional nonlinear
Lecture 21: Regular and singular perturbation theory.
Lecture 22: Asymptotic matching.
Lecture 23: Boundary layer-type perturbation theory.
Lecture 24: Mathematical structure of boundary layers.
Lecture 25: High order boundary layer theory.
Lecture 26: WKB theory.
Lecture 27: Summation of divergent series.
Final Exam (in class)