Full Name:
Signature:
Student Number:
Math 361 Final Exam
April 2009
2.5 hours.
Instructions: There are 7 pages in this test including this cover page.
Ensure that your full name and student number appear on this page.
No calculators, books, notes, or el
Lecture 6: Models described by two-variable nonlinear
differential equations
Yue-Xian Li
University of British Columbia
Math 361 September, 2016
Lecture 6: Models described by two-variable nonlinear differential equations p.1/?
A system of two nonlinear d
Lecture 5: Bifurcations in nonlinear systems
Yue-Xian Li
University of British Columbia
September, 2016
Lecture 5: Bifurcations in nonlinear systems p.1/19
Bifurcation point
Definition:
x = f (x, r),
where
x R is the phase variable,
r R is a control param
The Mathematics of Biological Pattern
Formation
Yue-Xian Li
University of British Columbia, Vancouver, Canada
The Mathematics of Biological Pattern Formation p.1/22
A preliminary schedule:
1. An introduction to biological patterns and related
mathematical
Lecture 4: Qualitative Method in the Analysis of 1D Nonlinear
Differential Equations
Yue-Xian Li
University of British Columbia
Math 361 September, 2016
Lecture 4: Qualitative Method in the Analysis of 1D Nonlinear Differential Equations p.1/15
Quick revi
Lecture 1. Linear Systems: Exponential Growth and Decay
University of British Columbia, Vancouver
Yue-Xian Li
September 8, 2016
1
A Model of Synchronized Cell Division
Consider a cell population that divides synchronously.
0
1
2
3
4
.
Figure 1: A model of
Lecture 3. Models in Population Genetics: Selection
University of British Columbia, Vancouver
Yue-Xian Li
September 19, 2016
1
Constructing a model
(1) Formulate the biological question.
(2) Determine the basic ingredients (model variables, parameters, co
Lecture 8. A Few Additional Topics in Nonlinear Dynamics
University of British Columbia, Vancouver
Yue-Xian Li
November 2016
1
Poincar
e-Bendixson Theorem:
Poincar
e-Bendixson Theorem: Suppose that
(1) R is a closed, bounded subset of the phase plane;
(2)
Lecture 2. Nonlinear Systems: Logistic Model
University of British Columbia, Vancouver
Yue-Xian Li
September 12, 2016
1
Summary of one-variable linear systems
Only three possible outcomes: exponential growth (to infinity), exponential decay (to zero), an
UBC Mathematics 361 Section 101
Midterm Exam (Nov 10, 2014)
Check: m361 mid 16 materials.txt for details of the materials covered.
This midterm was given in a previous year when materials covered differ from what we have covered this
year. So, do what wor
Full Name:
Student Number:
Signature:
Math 361 Final Exam
December 2006
2.5 hours.
Instructions: There are 7 pages in this test including this cover page. There should also be a spare page
at the end in case you need extra room for some answers.
Ensure th
Lecture 7: Models in molecular and cell physiology
Yue-Xian Li
University of British Columbia
Math 361 October, 2016
Lecture 7: Models in molecular and cell physiology p.1/46
7.1 Enzymes and enzyme catalyzed biochemical reactions
7.1.1 Enzymes.
Enzymes ar