AMATH 383 Solution #5
Winter 2010
Problem9.6
6. Foranopenaccessfishery,theprofitafishermancanearnisgovernedbythefollowing
equation:
P (t ) pH cE
Where H is the harvest rate governed by:
H (t ) qEN
The change in Effort expended by fisherman is directly p
AMATH 383 Solution #4
Winter 2010
Problem10.1
(a). The happiness of the husband and wife in marriage is heading towards the
equilibrium (x*,y*), determined by setting f(x*,y*)=0 and g(x*,y*)=0, where f and g are
the right-hand side of the differential equ
AMATH 383 Solution #3
Winter 2010
Problem9.1
(a). a=0, b=0, then
dx
dy
r ( x0 x), r ( y0 y).
dt
dt
Setting the right-hand side to zero yields the equilibrium solution:
x*=x0, y*=y0.
The stability consideration is rather easy because the equations can be
AMATH383SolutiontoAssignment#2
Winter2010
Problem1
To reproduce Table 3.3, it is important to be able to specify the number of decimal places
used in the calculation, not the number of decimal places displayed. In Excel one can use
the truncation command
AMATH383SolutiontoAssignment#1Winter2010
Problem2.4
a.
N c ( t ) m ( t ) / mc .
Ec d N c Ec d m.
dt
mc dt
Y Y0 ( m ) 3/ 4 .
Therefore the equation
Y Yc N c Ec
d
Nc
dt
Becomes:
Y0 ( m)3/4
Yc
Ed
m c m.
mc
mc dt
This is the same as:
Ym
Y
d
m ( 0 c )
AMATH 383 Homework Assignment #6
Assigned: Tuesday, February 23, 2010
Due in Class: Tuesday, March 2, 2010
Reproduce Figures 8.2, 8.3 and 8.4. Briefly derive the formulas that you need (You can follow that in the book). Use whatever programming language y
AMATH 383 Homework Assignment #5
Assigned: Tuesday, February 16, 2010
Due in Class: Tuesday, February 23, 2010
1. Do Problem 6 of Chapter 9.
2. Do Problem 1 of Chapter 11
3. Do Problem 2 of Chapter 11
Homework Assignment #4
Assigned: Tuesday, February 9, 2010
Due in Class: Tuesday, February 16, 2010
Problem 1. Do Problem 1 of Chapter 10.
Problem 2. Do Problem 2 of Chapter 10.
Problem 3. Do Problem 3 of Chapter 10.
AMATH 383 Homework Assignment #3
Assigned, Tuesday February 2, 2010
Due in Class, Tuesday February 9, 2010
1. Do Problem 1 in Chapter 9
2. Do Problem 4 in Chapter 9
3. Do Problem 5 in Chapter 9
AMATH 383 Homework Assignment #2
Assigned: January 26, 2010
Due in class: February 2, 2010
1. Do the problem posed on p64 and reproduce Table 3.3. There is a typo in that table; find that typo. Show your work.
2. Problem 6 in Chapter 6.
3. Problem 10 in C
AMATH 383 Homework Assignment #1
Assigned: January 19, 2010
Due in class: January 26, 2010
1. Problem 4, Chapter 2.
(Please note that there was a typo in the formula in part (c): M should be M1/4)
2. Problem 7, Chapter 2. Please show your assumptions and