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Math
31S  =
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bsp;  =
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bsp;  =
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bsp;  =
; Fall
2011
Tentative Schedule of Lecture=
s and
Examinations
W Aug.<=
span
style=3D'mso-spacerun:yes'> 31 A
conservation principle: One-compartment dilution
F &=
nbsp; Sep. 2 &=
nbsp; Recovering
a function from its rate of change
M &n=
bsp; Sep. 5 &=
nbsp; What
is a differential equation?
W Sep. 7 &=
nbsp; Review
of integration: The Fundamental Theorem of Calculus
F &=
nbsp; Sep. 9 &=
nbsp; The
natural logarithm function
M &n=
bsp; Sep. 12 The
natural logarithm function (continued)
W Sep. 14 The
exponential function
F &=
nbsp; Sep. 16 The
exponential function (continued)
M &n=
bsp; Sep. 19 Solving
first order differential equations
W Sep. 21 Separat=
ion
of variables
F &=
nbsp; Sep. 23 Linear
first order differential equations
M &n=
bsp; Sep. 26 Linear
first order differential equations with constant coefficients
W Sep. 28 Applications of
first order differential equations
F &=
nbsp; Sep. 30 Qualita=
tive
analysis of a first order equation.
M &n=
bsp; Oct. 3 &=
nbsp; Qualitative
analysis (continued)
W Oct. 5 &=
nbsp; Models
of population growth
F &=
nbsp; Oct. 7 &=
nbsp; Models
of population growth (continued)
M &n= bsp; Oct. 10 Review<= o:p>
W Oct. 12 Exam
1
F &=
nbsp; Oct. 14 The
logistic model of population growth
M &n=
bsp; Oct. 17 Fall
recess: No Classes
W Oct. 19 The
logistic model (continued)
F &=
nbsp; Oct. 21 Solving the logi=
stic
model: Partial fractions
M &n=
bsp; Oct. 24 Partial
fractions (continued)
W Oct. 26 Lineari=
zation
F &=
nbsp; Oct. 28 Integra=
tion
by parts
M &n=
bsp; Oct. 31 Integra=
tion
by parts (continued)
W Nov. 2 Principle =
of
linearized stability
F &=
nbsp; Nov. 4 Systems of
differential equations
M &n=
bsp; Nov. 7 Solving
systems of differential equations
W Nov. 9 Phase-plane
analysis: nullclines, equilibrium points and stability
F &=
nbsp; Nov. 11=
Phase-plane
analysis (continued)
M &n=
bsp; Nov. 14=
Population
models of two interacting species
W Nov. 16=
Predator-Prey
models: The Lotka-Volterra equations
F &=
nbsp; Nov. 18=
M &n=
bsp; Nov. 21=
Predator-prey
models continued
W Nov. 23=
Competition
and cooperation
F &=
nbsp; Nov. 25=
Thanksgivi=
ng
recess
M &n=
bsp; Nov. 28=
The
principle of competitive exclusion.
W Nov. 30=
Review
F &=
nbsp; Dec. 2 E=
xam
2
M &n=
bsp; Dec. 5 Revi=
ew
W Dec. 7 Revi=
ew
F &=
nbsp; Dec. 16=
Final
Examination