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Instructor:
Dr. Thomas Hillen
Office: CAB 575 , Phone: (780)
492
-
3395,
E-mail: thillen@ualberta.ca
To help me manage my email inbox, please include "MATH
372" in the subject line of any email message you send to me
Course web site: http://www.math.ualberta.ca/~thillen/fall10/math372.html
Office hours: Wed 2-3 in CAB 575, Fri 2-3 in Computer lab CAB 335
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Recommended textbook:
FR Giordano, WP Fox, SB
Horton, MD Weir, A First Course in Mathematical Modeling, 4th
ed., Brooks/Cole, 2009
Maple tutorial:
http://www.math.udel.edu/teaching/course_materials/driver/driver.html
| Date |
Material Covered / Special Event |
pdf files, maple files (some links are not yet working)
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Matlab
(coming soon)
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Sep
08, 10
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1. Introduction
(1.1) The five-step modelling process
(1.2) The automobile problem
(1.3) Sensitivity analysis
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TheModellingProcess.pdf
automobile.pdf
automobile.mws
automobile.html |
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Sep
13, 15, 17
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2 Differential Equations
(2.1) Motivation
(2.2) Probabilities and Rates
(2.3) Modelling with ODEs
(2.4) Phase line and vector field
(2.5) Linear Stability Analysis
(2.6) Existence and Uniqueness
(2.7) Some Case Studies
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Chapter 3 (chapter
3
of
G de Vries, T. Hillen, M. Lewis, J. Mueller,
B. Schoenfisch, A Course
in Mathematical Biology, SIAM, Philladelphia, 2006.
DE.pdf
steadystates.pdf
cooling.pdf
chemical.xls
tank.pdf
tank.xls |
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Sep
20, 22, 24
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3
Optimization
(3.1) Unconstrained single valued
optimization
(3.2) Whale population growth
(3.3) Unconstrained multi-variable optimization
(3.4) Constrained optimization and Lagrange
multipliers
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whale.html
LagrangeReview.pdf
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Sep 24
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Assignment 1 due
Choice of
Term Project |
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Sep
27, 29, Oct 01
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(3.5) The personal
computer problem
(3.6) Lagrange multipliers and Sensitivity
4. Discrete models
(4.1) Motivation
(4.2) Modelling with
discrete models
(4.3)
The
general
linear
model
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personalComputer.pdf
personalComputer.html
shadowPrice.pdf
Discrete-Problems.pdf
chapter2.pdf Chapter 2 of
G de Vries, T. Hillen, M. Lewis, J. Mueller, B. Schoenfisch, A Course
in Mathematical Biology, SIAM, Philladelphia, 2006.
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Oct
04, 06, 08
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(4.4) Cobwebbing and
Fixed Points
(4.5) Linear stability analysis
(4.6) The Discrete logistic equation
5.
Linear
programming
(5.1) The graphical method
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cobwebbing.mws
cobwebbing.html (Cobwebbing and
Bifurcation diagram)
discreteLogistic.xls
car-buy.html
sleep.pdf
carpenter.pdf
carpenter.html
linearprograms.pdf
LPSolve.pdf
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Oct
08
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Assignment 2 due |
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Oct
11,
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Thanksgiving, no
class |
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Oct
13,
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(5.2) The analytical method
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minimize.pdf
minimize.html
horse.pdf
horse.html
horse.xls
LPSolve2.pdf
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Oct
15
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Midterm in class
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Oct
18, 20, 22
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(5.3) Simplex method
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maximize.pdf
maximize.html
(these files are for reference; not
discussed in class)
excelSolverTutorial.ppt
excelSolverTutorial.pdf
The excel solver tutorial was written by former MATH 372 students!
cargo.pdf |
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Oct
25, 27, 29
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6 Systems
of ODEs
(6.1) steady states, phase plane analysis,
(6.2) linear stability
(6.3) Examples
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linearstability.pdf
Example of phaseplane
analysis in Maple |
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Nov
01, 03, 05
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7 Systems of discrete
equations
(7.1) Make higher order into a system
(7.2) Solution Theory
(7.3) General 2 x 2 systems
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see also chapter2.pdf
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Nov
05
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Assignment 3 due
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Nov 08, 10
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(7.4)
The
discrete
Zoo
(7.5) Linearization and Host Parasitoid Model
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Romeo and Juliet - applet
(thanks to Dr. de Vries and Cole S.)
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Nov
15, 17, 19
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8 Epidemic Models
chosen from
R_0, flu, H1N1 or Zombies, as time allows.
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Nov 22
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Term
Project:
draft version due |
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Nov
22, 24, 26, 29
Dec 01, 03, 06, 08
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Presentations
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Dec 08
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Term
Project:
final version due |
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Assignments / Projects /
Exams:
Assignments:
- Assignment 1, due Sep 24
in class.
Solutions
problem2b: pdf, mws
- Assignment 2, due
Oct 08
in class.
Solutions
exercise7.pdf
exercise8.pdf
p31-32.pdf
- Assignment 3, due Nov 05
in class.
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