The calendar below provides information on the course’s lecture (L), recitation (R) and exam (E) sessions.
| SES # | TOPICS | KEY DATES |
|---|---|---|
| L0 | Terminology and implicit solutions | |
| Unit I: First-order differential equations | ||
| L1 | Integration and solutions | |
| R1 | Recitation 1 | |
| L2 | Fundamental principles | |
| L3 | First-order linear equations | |
| R2 | Recitation 2 | |
| L4 | Separable equations | |
| R3 | Recitation 3 | |
| L5 | Linear fractional equations | Problem set 1 due |
| Unit II: Second-order linear equations | ||
| L6 | Second-order linear equations | |
| L7 | Mechanical oscillation | |
| R4 | Recitation 4 | |
| L8 | Uniqueness and the wronskian | Problem set 2 due |
| L9 | Separation and comparison theorems | |
| R5 | Practice midterm 1 | |
| E1 | Midterm 1 | |
| R6 | Recitation 6 | |
| L10 | The maximum principle | |
| Unit III: Higher-order linear equations | ||
| L11 | Higher-order linear equations | |
| R7 | Recitation 7 | |
| L12 | Solution bases | |
| R8 | Recitation 8 | |
| L13 | Inhomogeneous equations | Problem set 3 due |
| L14 | Stability | |
| R9 | Recitation 9 | |
| L15 | Wellposedness; introduction | |
| R10 | Recitation 10 | |
| L16 | Uniform convergence | Problem set 4 due |
| L17 | Uniqueness and continuity | |
| R11 | Practice midterm 2 | |
| E2 | Midterm 2 | |
| L18 | Remarks on wellposedness | |
| Unit V: The Laplace transform | ||
| L19 | Laplace transform | |
| L20 | Transform and differential equations: generalized solutions, application to ODEs | |
| R12 | Recitation 12 | |
| L21 | Step functions | Problem set 5 due |
| L22 | Convolution | |
| R13 | Recitation 13 | |
| L23 | The dirac distribution | |
| R14 | Recitation 14 | |
| L24 | The transfer function and the pole diagram | Problem set 6 due |
| Unit VI: The linear systems | ||
| L25 | Linear systems | |
| R15 | Recitation 15 | |
| L26 | Eigenvalues and eigenvectors | |
| R16 | Recitation 16 | Problem set 7 due |
| L27 | Complex solutions and the fundamental matrix | |
| R17 | Practice midterm 3 | |
| E3 | Midterm 3 | |
| L28 | Repeated eigenvalues and the matrix exponential | |
| L29 | Phase planes I | |
| L30 | Phase planes II | |
| L31 | Plane autonomous system | Problem set 8 due |
| L32 | Stability and almost linear systems | |
| L33 | Problems from ecology | |
| L34 | Methods of Lyapunov | Problem set 9 due |
| L35 | Nonlinear oscillations | |
| L36 | The Poincare-Bendixson theorem | |
| R18 | Recitation 18 | |
| E4 | Final exam | |
