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 |
|