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 |