Exam 1
Calculus for Biological Scientists II, Fall 2012
September 28, 2012
Name:
Be sure to justify all your answers and show your work.
Question Possible Points Points
1
15
2
15
3
20
4
18
5
14
6
18
Total:
100
1
1. (15 pts. total) Answer the following que
Homework 10 Solutions
Calculus for Biological Scientists II - Spring 2013
April 25, 2013
1. Separable. y =
1
x
2. Separable.
y = C0 e
x2
2
3. Separable. Use the u substitution u = ln y to get (ln y )2 = x2 /2 + C .
2
4. Integrating factor: M (x) = e2x . y
Homework 7 Solutions
Calculus for Biological Scientists II - Spring 2013
March 13, 2013
1. (a) xy -plane projection:
(b) xz -plane projection:
(c) yz -plane projection:
2. 8000 3 Nm
3. v (t) = ( sin(t), 4t, cos(t), s(t) =
4. (a) x y = x +
y
x
sin2 (t) + 1
Homework 4 Solutions
Calculus for Biological Scientists II - Fall 2012
February 13, 2013
1
1. a 1 , a R
1
2. 0. This is an upper triangular matrix, so you tell immediately that the determinant is nonzero.
3. (a) x = ei/3 , ei , ei5/3
(b) x = ei/4 , ei3/4
Homework 3 Solutions
Calculus for Biological Scientists II - Fall 2012
September 22, 2012
0
1. The value of the game is 0.5. The optimal strategies are: (0, 1, 0) and 0
1
2. (a) Linearly dependent. One possible linear combination is: 4(0, 1, 1) + 2(1, 2,
Homework 2 Solutions
Calculus for Biological Scientists II - Fall 2012
September 20, 2012
00
55
1. (a) AB =
5 4
4 6
(b) AB =
and BA =
12
24
and BA =
6 16
1 5
6
4 10 12
(c) AB = 0 4 1 and BA = 13
9
11 20 4
100
100
(d) AB = 0 1 0 and BA = 0 1 0
001
001
1/2
Homework 1 Solutions
Calculus for Biological Scientists II - Fall 2012
September 20, 2012
1.
(10x)4
4
+C
2.
f (x) = x3 + ex ln(3x2 ) sin(10x)
3
2
f (x) = 4 ex 10 cos(10x)
x
x
3. e2 + 1
4. 64 sin(2x) and (3)n e3x
5. Yes. x = 3 is a positive equilibrium.
6.
Exam 3
Calculus for Biological Scientists II, Fall 2012
December 7, 2012
Name:
Be sure to justify all your answers and show your work for full credit.
Question Possible Points Points
1
12
2
16
3
14
4
12
5
14
6
16
7
16
Total:
100
1
1. For each of the follo
Exam 2
Calculus for Biological Scientists II, Fall 2012
November 2, 2012
Name:
Be sure to justify all your answers and show your work for full credit. Do not approximate
answers.
Question Possible Points Points
1
18
2
18
3
18
4
18
5
14
6
14
Total:
100
1
1
Homework 11 Solutions
Calculus for Biological Scientists II - Fall 2012
May 2, 2013
1. Integrating factor: M (x) = ex . y = 2 + Cex
2. Integrating factor: M (t) = t4 . x = t4 ln t + Ct4
3. Method of characteristics. y = C1 e2t + C2 et
4. Method of charact