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Honors Differential Equations >> Content Detail



Calendar / Schedule



Calendar

The calendar below provides information on the course's lecture (L) and exam (E) sessions.


SES #TOPICSKEY DATES
L1Introduction, definitions and modeling
L2First-order linear equations, separable equations
L3First-order equations, Solution by quadrature
L4The initial value problem, uniqueness; the algebra of complex numbersProblem set 1 due one day after Ses #L4
L5Second-order linear equations
L6Undetermined coefficients
L7Stability criteria, the uniqueness theoremProblem set 2 due one day after Ses #L7
L8The Wronskian, sturm separation and comparison theorems
L9Green's function I: Initial value problem
L10Green's function II: Boundary value problemProblem set 3 due one day after Ses #L10
L11nth-order linear DEs with constant coefficients
L12Basis of solutions, the uniqueness theorem
L13Inhomogeneous equations, stability criteria
E1Midterm exam 1
L14Laplace transform: Basic properties
L15Laplace transform techniques; step functionsProblem set 4 due one day after Ses #L15
L16The Dirac delta and impulse functions, convolution
L17Generalized functions, the pole diagram
L18Plane autonomous systemsProblem set 5 due one day after Ses #L18
L19Linear autonomous systems
L20Wellposedness I
L21Wellposedness II: Picard's iteration method
L22Wellposedness III: Local theorems, Peano's existence theorem
L23Wellposedness IV: Strong continuity, bifurcation; exponential matrix
L24Phase portraits IProblem set 6 due one day after Ses #L24
L25Phase portraits II
E2Midterm exam 2
L26Stability
L27Methods of Lyapunov
L28Damped and undamped pendulumProblem set 7 due one day after Ses #L28
L29Limit cycles
L30Fourier series
L31The heat equationProblem set 8 due one day after Ses #L31
L32The wave equation, the Laplace equation
L33Sturm-Liouville systems
L34-37Reviews
E3Final exam

 








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