MATH 520: Foundations
of Analysis
Journal
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Review exercises:
p. 64 # 5
p. 91 #9
p. 104 #6
p. 112 #17
p. 118 #5
p. 128 #12 a)
p 144 #1 some, #2 b)
f,g diff. on R. Define h(x)= f(x) for x < a, and h(x)=g(x) for x >a.
What are the lateral limits of h when x tends to a? Does h'(a) exist?
What can you say about the lateral limits of
[f(x)-f(a)] /[x-a], x<a, and [g(x)-g(a)]/[x-a], x>a?
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Practice exercises from section 5, for the final.
Section 5.1: # 12 a).
Section 5.2: # 4, 10, 12.
Section 5.3: # 4, 5, 8, 9.
Section 5.4: # 1 f), 2 a), 3, 7, 8.
Final covers sections 3.4 through 5.4.
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HW 13 (due 5/6, 4:30 pm):
Section 5.1: # 12 c).
Section 5.2: # 12.
Section 5.3: # 4, 5, 9.
Section 5.4: # 1 f), 2 a), 3, 7.
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Spring 05 final
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HW 12 (due 4/29, 4:30 pm):
Section 4.4: # 1, 2, 3, 5, 6, 7 (justify your answer!), 8, 11.
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HW 11 (due 4/22, 4:30 pm):
Section 4.2: # 5, 6, 8 f).
Section 4.3: # 16, 17, 18, 21, 29, 31.
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HW 10 (due 4/15, 4:30 pm):
Section 3.6: #1 b), 2 d), 4, 5, 8, 9.
Section 4.1: #4, 6, 7 f), 11 a), 14.
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HW 9 (due 4/8, 4:30 pm):
Section 3.4: # 1 a), b), i), j); 2), 3) (do only h(x) ); 7 a).
Section 3.5: # 4, 6, 11, 13 (another numerical algorithm), 22 (this proof is essentially a numerical algorithm).
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HW 8 (due 4/1, 4:30 pm):
Section 3.1: # 1 d), 2 p), 3, 4, 9.
Section 3.2: # 1, 3, 6, 8 (part b) only), 9.
Section 3.3: # 1 e), 2, 4 d), e), 5. c), g), 7, 8.
Extra credit: Section 3.3 #9.
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HW 7 (due 3/11, 4:30 pm):
Section 2.5: # 8 b), 12, 13.
Section 2.6: # 2 c), 3, 4, 7, 8, 9.
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Practice exercises for the midterm:
1.3: #11 c)
1.4: #3
1.5: #13
2.1: #2 e), h);
2.2: #9,13
2.3: #12 a),
2.5: #9.
2.6: #4, 5
Proof of Thm 2.2.3 b).
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HW 6 (due 3/6, 4:30 pm):
Section 2.2: # 13, 15 a), c); 20, 22.
Section 2.3: # 6; 8 b), c) (long computation!); 9; 12.
Section 2.4: # 4; 7 a), b), c); 8.
Section 2.5: # 4 a), b), c); 7.
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HW 5 (due 2/26, 4:30 pm):
Section 2.1: #1 a); 2 c), h); 3; 6 a); 8; 11; 12; 14; 15.
Section 2.2: # 1 e), f); 2 d); 4; 6; 11 ( a) should be quick by contradiction!, b) probably too).
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HW 4 (due 2/19, 4:30 pm):
Section 1.5: (Note: I'll always write "sup" (supremum) for lub and "inf" (infimum) for the glb!!!)
#2a), b); 5; 6; 9 a), c) (give a proof or a counterexample in both a) and c) !) 10; 14; 15; 18, 19 a) and b); 21
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HW 3 (due 2/12, 4:30 pm):
Section 1.4: #1; 2 a); 3; 5; 9, 10, 13, 23.
.
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HW 2 (due 2/5, 4:30 pm):
Section 1.3: #1 all parts; 2; 4 a), b); 5; 8 d); 9 d), 11 d); 15.
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HW 1 (due 1/29, 4:30 pm):
Section 1.1: #3; 6 f), g); 7 a) (via a proof "by the element"); 8 c) and g); 15 (all parts).
Section 1.2: #3; 5 a), b), c); 6 b); 8 b), c), 9 (for 8 b) and c); 10 a), b), c).
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