semesters >
winter 2024 >
mth264 >
week 10
MTH-264 Week 10 (March 10-16)
semesters >
winter 2024 >
mth264 >
week 10 >
outline
Outline
5.1 Equilibrium Point Analysis
- recommended:
1, 5, 7, 8, 9, 14, 15, 16, 18, 22, 23, 24, 25
- the linear microscope
- focus on an equilibrium point
- zoom in
- the concept of linearization
- the revenge of the jacobian
- separatrices
5.2 Qualitative Analysis
- recommended:
1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 18, 20
- given a first-order system
- x ' = f(x,y)
y ' = g(x,y)
- nullclines
- x-nullcline: the set of points (x,y)
where f(x,y) = 0
- y-nullcline: the set of points (x,y)
where g(x,y) = 0
- equilibrium points lie at the intersections of x- and y-nullclines
- nullclines and separatrices separate region into subregions where solutions may have
uniform behavior
- nullclines are not necessarily straight lines
semesters >
winter 2024 >
mth264 >
week 10 >
assessments
Assessments
- Deadlines and File Submission
- All assessments are due by 11:59pm on the date indicated
- Assessments are submitted online to our
MTH-264 Assignments
folder.
- No late assessments are accepted.
- Homework
- due Thursday, March 14:
3.5 -
3.7 -
- due Thursday, March 21:
5.1 -
5.2 -
- due Thursday, March 28:
(none)
- Exams
- due Thursday, March 28: Exam 2
- Exam 2 (solutions)
- Exam 2 covers sections 3.1-3.5, 3.7, 5.1-5.2
- Exam 2 will be released by 11:59pm on Thursday, March 21 and is
due by 11:59pm on Thursday, March 28.
semesters >
winter 2024 >
mth264 >
week 10 >
handouts
Handouts
- Announcements
- Technology Tips
- Second-Order Linear Equations
- Linear Systems
semesters >
winter 2024 >
mth264 >
week 10 >
videos
Videos
- Linear Systems: Complex Eigenvalues
- Linear Systems: Bifurcation Cases
- Nonlinear Systems: Linearization
- all MTH-264 Videos
(YouTube playlist)
semesters >
winter 2024 >
mth264 >
week 10 >
technology
Technology
- Communication
- Desmos
- Excel
- Mathematica