Math 323 Homework


(Links are given to PDF files for homework solutions; click here to get Acrobat Reader to read these files.)

due Friday, Jan. 18:  p.10 #3, 4, 14, 16 and the initial value problem  y' + (sin t) y = 0, y(0)=1; 
p. 24 #2, 6, 10, 12 and the following problem:
Isotope A, which has a half-life of 3 hours, decays into isotope B, which has a half-life
of 10 hours.   If a sample initially contains 100g of isotope A and 50g of isotope B, how much
of isotope B will there be after 7 hours?

SOLUTIONS
 due Friday, Jan. 25: p.37 #6, 8, p. 66 #3,4,6,8, and the following problem:  The population of fish in a lake is 1000 in 1980 and 3000 in 1990. Predict the
population in 2010 using (a) the Malthusian model, and (b) the logistic model, with the extra
information that the population is 4500 in the year 2000.


SOLUTIONS

due Friday, Feb. 1:  p.80 # 1,2,4,14,16,18; p.105 #2,4

SOLUTIONS

due Friday, Feb. 8:  p.136 # 2,5,8,13; p.140 #2,5,6,10,12; p.144 #3,6,10; p.149 #2,6

SOLUTIONS
due Friday, Feb. 22:  p.149 #12, 20; p.156 #4, 6; p.164 #1, 5, 6, 11, 13; p. 172 #1

SOLUTIONS
due Friday, Feb. 29: p.172 #4,5, 8, 11 (note correction!); p. 197 # 1,2,3,7;
and the following extra problem:
When attached to a spring, a 300g mass stretches the spring by 20cm.  If the mass is pulled
down by another 1/4 metre, and released with a downward velocity of 1 m/s, find
(i) the period of the resulting motion;
(ii) the maximum height above equilibrium that the mass reaches; and
(iii) the first time that the mass passes through the equilibrium position.

SOLUTIONS
due Friday, Mar. 21: p.216 #2, 10; p.232 #4, 17, 19; p.237 #3,4,10,13,15,23
(Note that the answer in the back of the book for #15 is incorrect---the cosine should be a sine.)

SOLUTIONS
due Friday, Mar. 28: p. 243 #3, 9, and the following problem:
Suppose that f(t) = 5 for 0 < t < 10 and f(t)=t for t>10.  Compute the Laplace transform of f(t)
in two ways---using the definition, and by expressing f(t) in terms of a Heaviside step function.

SOLUTIONS
due Friday, April 4:  p. 340 #2,8,12; p.344 #3,6,9; p.352 #1,6,17

SOLUTIONS
due Friday, April 19: p.366 #2, 6, 8; p.377 #1, 4, 11; p. 393 #3, 4, 14

SOLUTIONS