|
|
||
| Date |
Section |
Topics |
| 3/30 |
4.1 |
Simple Harmonic Motion. Solution to the Undamped Unforced Oscillator |
| 4/1 |
4.1 |
Component forms & Single
wave forms |
| 4/3 |
4.2 |
Characteristic Equations and
roots of DEs. Real Characteristic roots. |
| 4/6 |
4.3 |
Complex roots |
| 4/8, 4/10 |
4.4 |
Undetermind Coefficients |
| 4/13 |
4.5 |
Variation of Parameters |
| 4/15 |
4.6 |
Forced Osillations; Resonance;
Beats |
| 4/17 |
4.7 |
Energy; Conservative
systems Conversion from Higher order DEs to Systems of 1st order DEs. |
| 4/20 |
5.1 |
Linear Transformations |
| 4/22 |
5.2 |
Kernel; Image; Rank |
| 4/24 |
5.3 |
Eigenvalues, Eigenvectors, and
Eigen-spaces. |
| 4/27 |
Examples of Eigenvalues,
Eigenvectors |
|
| 4/29 |
Dimension theorem; Linear
independence of Eigenvectors |
|
| 5/1 |
Midterm |
|
| 5/4, 5/6 |
5.4 |
Coordinates relative to a basis;
Diagonalization; Decoupling DEs. |
| 5/8 |
6.1 |
Systems of Linear First Order DEs |
| 5/11 |
6.2 |
Linear system with real
eigenvalues: distinct & repeated eigenvalues; Phase Portraits; Stable/Unstable Equilibrium Solutions |
| 5/13 |
6.3 |
Linear Systems with complex
Eigenvalues |
| 5/15 |
More phase portraits Real nonzero Distinct E-values Complex Conjugate E-values Borderline Cases |
|
| 5/18 |
6.4 |
Phase Plane Portraits for
degenerate cases: zero eigenvalues & repeated eigenvalues |
| 5/20 |
6.7 |
Nonhomogeneous Linear Systems:
Variation of Parameters |
| 5/22 |
6.7, 6.5 |
Nonhomogeneous Linear Systems::
Undetermined Coefficients Decoupling a system of DEs |
| 5/27 |
7.1 |
Nonlinear Systems: Equilibrium
points. h- and v- nullclines. Suggested Exercises: 7.1 #10-13, 27-30 |
| 5/29, 6/1 |
7.2 |
Nonlinear system: Jacobian
matrix and Linearization. Classification and stability of Equilibrim points Suggested Exercises: 7.2 #3-5, 6-10 |
| 6/3, 6/5 |
Review |
|
| 6/9 |
Final Exam |
|