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
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
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
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 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 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 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
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 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
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
If predators and their prey are spatially distributed it is obvious that there will be temporal spatial
variations in the populations as the predators move to catch the prey and the prey move to evade
the predators. Travelling bands have been observed in
Mathematical models are a powerful
method to understand and control
the spread of Huanglongbing
Rachel A. Taylor1, Erin A. Mordecai2, Christopher A. Gilligan3,
Jason R. Rohr1 and Leah R. Johnson1,4
1
Department of Integrative Biology, University of South
Graph Theory and Networks in Biology
Oliver Mason and Mark Verwoerd
March 14, 2006
Abstract
In this paper, we present a survey of the use of graph theoretical techniques in Biology. In
particular, we discuss recent work on identifying and modelling the st
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
There is a long history of applying partial differential equations to spatio-temporal
pattern formation in morphogenesis, as pioneered by Alan Turing and Hans
Meinhardt. Advanced imaging techniques such as fluorescence recovery after
photobleaching (FRAP)
One application of mathematical models is in analyzing the workings of the
mammalian circadian clock. About 20,000 synchronized neurons in the
suprachiasmatic nucleus (SCN) control daily rhythms of physiology, metabolism and
behavior. In addition, almost
CAN BIOLOGY LEAD TO NEW THEOREMS?
BERND STURMFELS
Abstract. This article argues for an affirmative answer to the question in the
title. In future interactions between mathematics and biology, both fields will
contribute to each other, and, in particular,
Mathematical Biology is
Good for Mathematics
Michael C. Reed
A
bout ten years ago I wrote an article,
Why is Mathematical Biology so Hard?
for these Notices intending to explain
why the applications of mathematics to
biology would be very different than t
Hindawi Publishing Corporation
Abstract and Applied Analysis
Volume 2014, Article ID 289349, 9 pages
http:/dx.doi.org/10.1155/2014/289349
Research Article
Stability of a Mathematical Model of
Malaria Transmission with Relapse
Hai-Feng Huo and Guang-Ming Q
Hindawi Publishing Corporation
BioMed Research International
Volume 2014, Article ID 902545, 9 pages
http:/dx.doi.org/10.1155/2014/902545
Review Article
Modeling Biology Spanning Different Scales: An Open Challenge
Filippo Castiglione,1 Francesco Pappalar
J Biol Phys (2006) 32: 335353
DOI 10.1007/s10867-006-9019-7
RESEARCH PAPER
Modelling the Human Immune System by Combining
Bioinformatics and Systems Biology Approaches
Nicolas Rapin & Can Kesmir & Sune Frankild &
Morten Nielsen & Claus Lundegaard &
Sren B
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