The calendar below provides information on the course's lecture (L), recitation (R) and exam (E) sessions.
Course calendar.
| 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 |
|
