TMA4225 Foundations of analysis: Fall term 2013
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 \(F\)? |
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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 |
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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 |