| Feb. 4., 2019: |
Introduction, Overview, First example:
Newton's law of cooling (Brannan/Boyce, Section 1.1)
|
| Feb. 6., 2019: |
Integrating factors and separation of
variables (Brannan/Boyce, Sections 1.2 and 2.1)
|
| Feb. 12., 2019: |
Detailed discussion of
long-time behavior, modeling examples (Brannan/Boyce, Section 2.2)
|
| Feb. 13., 2019: |
Differerence between linear and nonlinear
equations; existence, uniqueness; examples of non-uniqueness and
blow-up (Brannan/Boyce, Section 2.3)
|
| Feb. 19., 2019: |
Population dynamics and logistic growth;
optimal harvesting
(Brannan/Boyce, Section 2.4)
|
| Feb. 20., 2019: |
Exact equations (one example), elementary
discussion of numerical methods (Brannan/Boyce, selected topics
from Sections 2.5-2.7)
|
| Feb. 26., 2019: |
Exact equations and integrating
factors (Brannan/Boyce, Section 2.5)
|
| Feb. 27., 2019: |
Numerical methods (Brannan/Boyce,
Section 2.6)
|
| Mar. 5., 2019: |
Trapezoidal rule and Runge-Kutta methods (Brannan/Boyce, Section 2.7)
|
| Mar. 6., 2019: |
Crash course in Linear Algebra I (Brannan/Boyce, Section 3.1)
|
| Mar. 12., 2019: |
Crash course in Linear Algebra I
|
| Mar. 13., 2019: |
Systems of two first-order linear
equations (Brannan/Boyce, Section 3.2 and 3.3)
|
| Mar. 19., 2019: |
Systems of two first-order linear
equations, complex and repeated eigenvalues (Brannan/Boyce, Section 3.4 and 3.5)
|
| Mar. 20., 2019: |
Midterm review
|
| Mar. 26., 2019: |
Midterm Exam
|
| Mar. 27., 2019: |
Second order linear equations
I (selected topics from Brannan/Boyce, Chapter 4)
|
| Apr. 2., 2019: |
Second order linear equations
I (selected topics from Brannan/Boyce, Chapter 4)
|
| Apr. 3., 2019: |
The Laplace transform (Brannan/Boyce,
Section 5.1 and 5.2
|
| Apr. 9., 2019: |
The inverse Laplace transform (Brannan/Boyce,
Section 5.3)
|
| Apr. 10., 2019: |
Solving
differential equations via the Laplace transform (Brannan/Boyce,
Section 5.4
|
| Apr. 23., 2019: |
TBA
|
| Apr. 24., 2019: |
Discontinuous and periodic functions,
applications to forcing (Brannan/Boyce,
Sections 5.5-5.7
|
| Apr. 30., 2019: |
Convolution Integrals, linear systems, and
feedback control (selected topics from Brannan/Boyce,
Sections 5.8 and 5.9)
|
| May 7., 2019: |
Linear stability (Brannan/Boyce,
Section 7.1
|
| May 8, 2019: |
Almost linear systems (Brannan/Boyce,
Section 7.2
|
| May 14, 2019: |
Predator-prey systems (Brannan/Boyce,
Section 7.3 and 7.4)
|
| May 15, 2019: |
Final exam review
|
| TBA: |
Final Exam, Room TBA
|