The calendar below provides information on the course's lecture (L) and exam (E) sessions.
Course calendar.| SES # | TOPICS | KEY DATES |
|---|
| L1 | Introduction, definitions and modeling | |
| L2 | First-order linear equations, separable equations | |
| L3 | First-order equations, Solution by quadrature | |
| L4 | The initial value problem, uniqueness; the algebra of complex numbers | Problem set 1 due one day after Ses #L4 |
| L5 | Second-order linear equations | |
| L6 | Undetermined coefficients | |
| L7 | Stability criteria, the uniqueness theorem | Problem set 2 due one day after Ses #L7 |
| L8 | The Wronskian, sturm separation and comparison theorems | |
| L9 | Green's function I: Initial value problem | |
| L10 | Green's function II: Boundary value problem | Problem set 3 due one day after Ses #L10 |
| L11 | nth-order linear DEs with constant coefficients | |
| L12 | Basis of solutions, the uniqueness theorem | |
| L13 | Inhomogeneous equations, stability criteria | |
| E1 | Midterm exam 1 | |
| L14 | Laplace transform: Basic properties | |
| L15 | Laplace transform techniques; step functions | Problem set 4 due one day after Ses #L15 |
| L16 | The Dirac delta and impulse functions, convolution | |
| L17 | Generalized functions, the pole diagram | |
| L18 | Plane autonomous systems | Problem set 5 due one day after Ses #L18 |
| L19 | Linear autonomous systems | |
| L20 | Wellposedness I | |
| L21 | Wellposedness II: Picard's iteration method | |
| L22 | Wellposedness III: Local theorems, Peano's existence theorem | |
| L23 | Wellposedness IV: Strong continuity, bifurcation; exponential matrix | |
| L24 | Phase portraits I | Problem set 6 due one day after Ses #L24 |
| L25 | Phase portraits II | |
| E2 | Midterm exam 2 | |
| L26 | Stability | |
| L27 | Methods of Lyapunov | |
| L28 | Damped and undamped pendulum | Problem set 7 due one day after Ses #L28 |
| L29 | Limit cycles | |
| L30 | Fourier series | |
| L31 | The heat equation | Problem set 8 due one day after Ses #L31 |
| L32 | The wave equation, the Laplace equation | |
| L33 | Sturm-Liouville systems | |
| L34-37 | Reviews | |
| E3 | Final exam | |