TMA4225 Foundations of analysis: Fall term 2013

A photo from the sea.

Exercises

In reverse chronological order. The solutions (except for #8) are by an anonymous student, occassionally tweaked and twisted (the solution, not the student) by me.

Week # § pp. Exercises Solution
47 13 8.4 299–301 49, 57, 58
6.2 199–200 23, 33, 37
Does problem 37 generalize to absolutely continuous \(F\)?
5.5 176–177 93
46 12 8.3 291–292 33 (Hint: rapid oscillations.)
8.4 299–301 48, 52, 55
Examination August 2013, problems 5, 6
45 11 8.1 280–281 17
Examination August 2013, problems 1–3
See the left margin
And one more exercise
44 10 4.1 119–121 14, 15
5.5 176–177 94
6.3 210–212 53
6.4 220–223 64
43 9 6.1 190–191 19, 20
6.3 210–212 42, 43, 45, 51
42 8 5.3 164–165 51, 52, 58, 61, 63 solution
5.4 172–173 67, 74, 81, 82
41 7 4.2 127–129 23
4.3 137–139 45, 46
Hint: \(\lim_{t\to a} h(t)=\lim_{n\to\infty} h(t_n)\) where \(t_n\to a\).
5.1 149–151 12, 13, 16, 17
5.2 156–158 21, 22
40 6 4.1 119–121 11, 12, 13
4.2 127–129 26
39 5 3.4 107–109 33, 35, 43, 44, 49–51
38 4 2.6 76–78 81, 82, 96
3.1 88–89 6, 8, 12
3.2 94 17–18
Two exercises not in the book
37 3 2.4 59–60 59 solution
2.5 66–67 67, 71, 74, 75
2.6 76–78 83
36 2 2.1 34–35 9 Solution
2.2 44–46 21, 27–29, 32, 33, 37
2.3 52–53 38, 49
35 1 1.1 9–10 8 Solution
1.2 17 19, 21
1.3 21–22 28, 30
1.4 26–27 40, 42, 47, 52
2013-11-20, Harald Hanche-Olsen