Math 304-200 Summer II, 2010
Assignments
Assignment 1
- Read sections 1.1-1.4
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 1.1 (pg. 11): 1(c), 6(g), 7
- Section 1.2 (pg. 25): 3(e,f), 5(l), 6(b), 8, 13
- Section 1.3 (pg. 57): 1(c), 2(b,c), 7(b)
Due Thursday, July 8, 2010
Assignment 2
- Read sections 2.1-2.3
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 1.3 (pg. 57): 10, 13, 16
- Section 1.4 (pg. 69): 3(c), 6, 9(b(i)), 10(e,g)
Due Monday, July 12, 2010
Assignment 3
- Read sections 2.3 and 3.1
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 2.1 (pg. 96): 3(e,g), 4(b,d) (By inspection means that
you use one of the properties of determinants, rather than calculate
things directly.)
- Section 2.2 (pg. 103): 1(b,c), 2(a), 3(c,d) (In 3, use row
reduction methods.), 9(a,b,c)
Due Wednesday, July 14, 2010
Assignment 4
- Read sections 3.2 and 3.3
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 2.2 (pg. 103): 5, 7
- Section 2.3 (pg. 109): 1(c), 2(e) (In 2(e), just find
x3, not the whole solution.), 3
- Section 3.1 (pg. 121): 16
- Section 3.2 (pg. 131): 2
Due Monday, July 19, 2010
Assignment 5
- Read sections 3.4 and 3.5
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 3.2 (pg. 131): 4(b), 6(a,d,e), 9(b,c), 10(e), 14(c)
- Section 3.3 (pg. 144): 2(c), 4(c)
Due Wednesday, July 21, 2010
Assignment 6
- Read sections 3.6, 4.1 and 4.2
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 3.3 (pg. 144): 6(a,d)
- Section 3.4 (pg. 150): 2(a,b,e), 8, 10
- Section 3.5 (pg. 161): 3, 4, 10
- Section 3.6 (pg. 167): 1(c), 2(c)
- Additional problem. Let B=[1,x,x2] be the standard
ordered basis for P3. If p(x) =(2x+1)2 and q(x)
= 3x−1, then find the coordinate vectors [p]B,
[q]B, [2q−p]B.
Due Monday, July 26, 2010
Assignment 7
- Read sections 4.3, 6.1
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 3.6 (pg. 167): 3, 10 (Hint: you will need a basis for the null
space of A).
- Section 4.1 (pg. 182): 1(c), 3, 4, 5(a,c), 9(a,b), 17(a,c), 19(a)
- Additional problem. Let A be the matrix given below. Find
bases for the row space, null space, and column space of A. What is
the rank of A? What is the nullity of A? Does the sum rank(A) +
nullity(A) equal what it should theoretically be?
1 | -2 | 3 | 3 |
2 | -5 | 7 | 3 |
-1 | 3 | -4 | 3 |
Due Wednesday, July 28, 2010
Assignment 8
- Read sections 6.2 (Application 2), 6.3 (Up to Application 1),
5.1, 5.4
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 4.2 (pg. 196): 4, 5(c), 10(d), 13, 15.
- Section 4.3 (pg. 204): 2, 5, 6, 11
- Section 6.1 (pg. 310): 1(a,c,e,g), 3
Due Monday, August 2, 2010
Assignment 9
- 5.3, 5.5, 5.6
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 6.1 (pg. 310): 2, 11
- Section 6.3 (pg. 340): 1(a,d), 2(a,d), 7, 20
- Additional problem: Consider the spring system shown in
Fig. 6.2.2. In class on Monday we derived equations for the system
where the spring constants k1, k2,
k3 were (possibly) unequal. Find the normal modes and
normal frequencies for this system when k1 =
k3=1, k2 = 3, and the masses are m1
=m2=1.
Due Wednesday, August 4, 2010
Assignment 10
- Problems. (Answers alone are not sufficient. You must (briefly)
explain how you arrived at them.)
- Section 5.1 (pg. 224): 15, 16
- Section 5.3 (pg. 243): 5, 6
- Section 5.4 (pg. 252): 1, 7, 8, 9
- Section 5.5 (pg. 270): 2, 8, 27
Due Monday, August 9, 2010