[E-K] is the textbook by Edelstein-keshet,

[S] is the notes written by Shi (available at CourseInfo:course
documents)

[PBA] is the segment of textbook by Polking, Boggess
and Arnold

(available at CourseInfo:course documents)

[BC] is a book by Brauer and Castillo-Chavez "Mathematical
Models

in population biology
and epidemilology"

** 8/30** Concept of DE, ODE, initial value problem

Malthus exponential model, Logistic model

Reading: [E-K] page 115-120, 212-215, [PBA] page 123-130

[S] Notes 1 page 1-2

Web reading:

http://www.sosmath.com/diffeq/modeling/modeling.html

http://www.sosmath.com/diffeq/first/application/population/population.html

** 9/4** Solve simple equations

Graphing the equations: direction fields and softwares

Reading: [S] Notes 2 [E-K] page 165-171

Web-reading:

http://www.sosmath.com/diffeq/first/separable/separable.html

http://www.sosmath.com/diffeq/slope/slope1.html

Web-software:

http://math.rice.edu/~dfield/ (click DFIELD 2001.2)

http://www.aw.com/ide/Media/MainMenu/Part1.html (Try 2 and 3)

Homework 1: (due 9/6)

[E-K] page 152: (1 or 2), page 257: 2(c), [PBA] page 134: 1,3,9,11,

Other problems:

(1) Solve P'=sin(t) (P+1), P(0)=1

(2) Slove P'=-y^2, y(0)=0.5

(3) the problem at http://www.sosmath.com/diffeq/first/separable/example2/example.html

(4) the problem at http://www.sosmath.com/diffeq/slope/example1/example.html

(note: answer is available online for (3)
and (4))

(5) Use computer to generate the direction field of dP/dt=P(10-P)-sin(t),
submit a printout

of the graph (hint: choose appropriate
window)

9/6: Phase line, Euler method

Reading: [S] Notes 2, [E-K] page 212-215

Web-reading:

http://www.sosmath.com/diffeq/first/phaseline/phaseline.html

http://www.sosmath.com/diffeq/first/numerical/numerical.html

Optional Web-reading:

(1) Original paper by Malthus (in Course Document folder)

(2) An article about Velhust's logistic equation (in Course Document
folder)

Web-software:

http://mss.math.vanderbilt.edu/~pscrooke/MSS/euler.html
(do Euler's method)

http://math.rice.edu/~dfield/ (click DFIELD 2001.2)

9/11: Data fitting, and Allee effect

[PBA] page 131-134, 138-142

Optional Web-reading:

(1) Original book by Gause (http://www.ggause.com/Contgau.htm), especially
chapter IV

Web-software:

http://www.btinternet.com/~endeavour/stats.html (do linear regression)

http://www.phys.unsw.edu.au/3rdyearlab/graphing/graph.html (another
linear regression)

Homework 2: (due 9/13)

(1) [E-K] page 152 (5d,e,f)

(2) [E-K] page 257 (3) Find the phase lines, equilibrium solutions,
and sketch a few solutions on direction fields.

(3) [PBA] page 135 (8)

(5) [PBA] page 136 (13) estimate k and N using the method introduced
in class

(6) [PBA] page 137 (14) estimate k and N using the method introduced
in class

(7) Compute by hand using Euler's method: y'=t+y, y(0)=1, step size=0.1,
n=5. Check your answer using the internet software.

9/13: Nondimensionalization and harvesting

Readings: [S] Notes 1 and 3

9/18: Stability, bifurcation and harvesting

Readings: handout in class (page 28-32 of [BC])

Web-Reading:

http://www.sosmath.com/diffeq/first/phaseline/phaseline.html (about
stability of equilibrium pts)

http://www.sosmath.com/diffeq/first/bifurcation/bifurcation.html (about
bifurcation and harvesting)

http://math.bu.edu/DYSYS/ode-bif/ode-bif.html (stability, bifurcation
and harvesting)

Homework 3: (due 9/20)

(1) [PBA] page 135 (10a,b)

(2) [PBA] page 135 (15)

(3) [PBA] page 138 (18,19,20)

(4) [E-K] page 258 (6)

(5) [S] Notes 3 (exercises 1,2,3)

(6) Solve the following logistic equation with harvesting:

P'=4P(1-P/4)-3, P(0)=2.

9/20: Outbreak of spruce budworm

Reading: [PBA] page 158-161

Webreading: Paper on spruce budworm at courseinfo(a huge pdf file)

http://www.entomology.umn.edu/cues/dx/sk/spruce2.htm (pictures of Budworm)

http://www.ento.vt.edu/~sharov/PopEcol/lec13/chorist.html (pictures
of Budworm)

http://www.na.fs.fed.us/spfo/pubs/fidls/sbw/budworm.htm

(an article from US Department of Agriculture Forest Service)

Websoftware: http://mss.math.vanderbilt.edu/~pscrooke/MSS/plotseveral.html

(maybe useful for you in other situations, it draws graphs of functions)

9/25: Computer Lab and Test 1 (take home)

No homework this week, Test 1 due 9/28.

9/27: Outbreak of spruce budworm

10/2: Comments on test problems. Predator-prey models.

10/4: Mathematics of systems: phase portrait, equilibrium points, nullclines,

10/9: Mathematics of systems: linearizations, types of equilibrium
points, periodic solutions, separatrices.

Reading: [E-K] page 171-193

Web reading: (if you have not taken Math 302)

http://www.sosmath.com/diffeq/system/linear/basicdef/basicdef.html

http://www.sosmath.com/diffeq/system/linear/graphical/graphical.html

http://www.sosmath.com/diffeq/system/linear/eigenvalue/eigenvalue.html

http://www.sosmath.com/diffeq/system/linear/qualin/qualin.html

Web software:

ttp://math.rice.edu/~dfield/ (click PPLANE 2001.2)

Homework 4: (due 10/11)

(1) [E-K] page 201 (5a,b,e) (hand drawing, also draw the arrows in the
regions bounded by nullclines)

(2) [E-K] page 201 (6a,b,e)

(3) [E-K] page 201 (7a,b,e)

(4) [E-K] page 201 (9)

10/11: Analysis of predator-prey and competition models.

10/18: Chemotaxis model (1)

Homework 5: (due 10/25)

(2) [E-K] page 201 (6a,b,e)

(3) [E-K] page 201 (7a,b,e)

(4) [E-K] page 201 (9)