October 9th: First order, linear, non-homogeneous equations: Population models, Newton's Law of Cooling, Integrating factors, particular solutions, variation of parameters
October 16th: First order, nonlinear equations: Logistic growth, separable equations and existence/uniqueness
Second order ODE
October 23rd: Second order, constant coefficient, homogeneous equations: LRC circuits, Newton's Second Law
October 30th: Second order, non-homogeneous equations: Forced-systems, Resonance, Particular solutions (non-homogeneous)
November 6th: Second order, homogeneous equations: Reduction of order, general theory, the Wronskian
November 13th: Second order, non-homogeneous equations: Variation of parameters
November 20th: Midterm in-class examination [there may be schedule changes due to class progress]
November 27th: Laplace transforms for ODE I: Heaviside functions, switches
December 4th: Laplace transforms for ODE I: Dirac delta functions, impulses
Systems of ODE
December 11th: Higher order equations and constant coefficient systems (I): eigenvalues, eigenvectors (distinct and complex roots of the characteristic equation)
December 18th: Higher order equations and constant coefficient systems (II): repeated roots of the characteristic equation, matrix exponential form
Geometric theory
January 8th: 2x2 linear constant coefficient systems (I) : Phase lines and phase planes
January 15th: 2x2 linear constant coefficient systems (II) : Null-clines, direction fields; Applications: mechanical systems,
[If time allows, we may also study some series solutions to ordinary differential equations]
January 22nd: Final in-class examination and review