TMA4225 Analysens grunnlag
Høsten
2007
Beskjeder:
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Please
find the grades for the exam posted below.
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Foreleser:
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Christian Skau.
Rom 1050, Sentralbygg II.
Telefon 73 59 17 55.
E-post: csk@math.ntnu.no
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Forelesninger:
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Tirsdag 12.15 - 14.00, F4
Onsdag 14.15 - 16.00, F3
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Øvinger:
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Torsdag 10.15 - 11.00, F6
30.08.2007
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Øving 1
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Chapter 1.6 (p. 37-38): 1,
2, 3, 4
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06.09.2007
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Øving 2
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Chapter 1.6 (p. 40-41): 9,
10, 11, 14, 15
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11.09.2007
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Øving 3
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Chapter 1.6 (p42-44): 16,
19, 20, 21, 24, 26, 27, 32, 33.
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20.09.2007
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Øving 4
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Chapter 1.6 (p. 45): 34, 35,
36
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27.09.2007
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Øving 5
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Chapter 1.6 (p 42-43) 17,
18, 22, 25
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04.10.2007
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Øving 6
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Mid.term exam.
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11.10.2007
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Øving 7
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Chapter 1.6 (p. 44) : 28, 29, 30;
Chapter 1.7 (p. 47): 4
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18.10.2007
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Øving 8
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Chapter 2.5: 3, 4, 6, 8, 11
(p.90-91)
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25.10.07
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Øving 9
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Chapter
2.5: 9, 12 (p. 91-92).
Problem: Prove that there exists a 100 meter race
between runners A and B, such that at each point x ∈ [0,100], runner A will have
10 times the speed of runner B, and yet runner B wins the race. In fact, one can construct the race
such that B is clocked at time T, while A is clocked at time 2T. [Hint: Use the Cantor set C and a
Cantor-like set Ĉ (of positive measure) in [0,T]
and [0,2T], respectively, such that runner A has zero speed at C and
runner B has zero speed at Ĉ.]
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01.11.07
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Øving
10
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Chapter 2.5: 7, 10, 15, 17
(p. 91-93)
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08.11.07
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Øving 11
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Chapter
2.5: 13, 18, 19, 21 a, b, c (p. 92-94)
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15.11.07
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Øving
12
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Chapter
6.7: 1, 2, 3 (p.312)
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22.11.07
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Øving
13
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Chapter
3.5: 10, 11,12, 20 (p.147-149)
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Treffetid:
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Treffetid: Torsdag 11.15 - 12.00.
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Lærebok:
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Stein
& Shakarchi: Real Analysis (Princeton Univ.
Press, 2005)
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Endelig pensum:
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Chapters
1 (except Sect.5), Chapter 2 (except Sect.4), Chapter 3.3, Chapter 6.1
& 2.
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Midtsemesterprøve:
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Tirsdag 2.oktober, 12.15 – 14.00, F4
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Eksamen:
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4. desember 2007, 4 timer, skriftlig.
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Grades
for the exam in TMA4225 (the midterm exam taken into account):
661338
A
661595 B
669001 E
670594 F
673095 A
673881 F
674801 D
676348 A
676458 A
676487 A
676492 A
685975 C
695546 B
696754 C
700836 E
701468 C
701469 F
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