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week 10
MTH-264 Week 10 (March 9-15)
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outline
Outline
3.7 The Trace-Determinant Plane
- recommended:
3,
4,
5, 7,
8,
9,
10,
11,
12,
13
- sinks, sources, saddles
- the borderline cases
- bifurcation of systems
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 2025 >
mth264 >
week 10 >
assessments
Assessments
- Deadlines and File Submission
- Submit your assessment as a single PDF file to the Assessment Folder
inside your assigned Google Drive folder by 11:59pm on the date indicated.
- No late assessments are accepted. If you have a conflict with a deadline,
contact me before the deadline.
- Solutions are posted under these links after the deadline.
- Homework
- due Wednesday, March 12:
3.2 - 23 alt,
3.3 - 20 alt,
3.4 - 12 alt,
3.5 - 7 alt,
17 alt,
23 alt
- due Wednesday, March 19:
3.7 - 7 alt,
9 alt,
5.1 - 26 alt,
5.2 - 13 alt
- due Wednesday, March 26:
(none)
- Exams
- due Wednesday, March 26: Exam 2
- Exam 2
(preview)
(solutions)
- Exam 2 covers sections 2.4, 2.5, 2.7, 3.1-3.5, 3.7, 5.1, 5.2
- A preview will be released by 10:59pm on Wednesday, March 19
and Exam 2 will be written in class on Wednesday, March 26.
semesters >
winter 2025 >
mth264 >
week 10 >
handouts
Handouts
- Announcements
- Technology Tips
- Second-Order Linear Equations
- Linear Systems
semesters >
winter 2025 >
mth264 >
week 10 >
videos
Videos
- Linear Systems: Complex Eigenvalues
- Linear Systems: Bifurcation Cases
- Nonlinear Systems: Linearization
semesters >
winter 2025 >
mth264 >
week 10 >
technology
Technology
- Communication
- Desmos
- Excel
- Mathematica