# TMA4225 Analysens grunnlag

Høsten 2007

Beskjeder:

Foreleser:

Christian Skau.
Rom 1050, Sentralbygg II.
Telefon 73 59 17 55.
E-post: csk@math.ntnu.no

Forelesninger:

Tirsdag 12.15 - 14.00, F4
Onsdag 14.15 - 16.00, F3

Øvinger:

Torsdag 10.15 - 11.00, F6

 30.08.2007 Øving 1 Chapter 1.6 (p. 37-38): 1, 2, 3, 4 06.09.2007 Øving 2 Chapter 1.6 (p. 40-41): 9, 10, 11, 14, 15 11.09.2007 Øving 3 Chapter 1.6 (p42-44): 16, 19, 20, 21, 24, 26, 27, 32, 33. 20.09.2007 Øving 4 Chapter 1.6 (p. 45): 34, 35, 36 27.09.2007 Øving 5 Chapter 1.6 (p 42-43) 17, 18, 22, 25 04.10.2007 Øving 6 Mid.term exam. 11.10.2007 Øving 7 Chapter 1.6 (p. 44) : 28, 29, 30; Chapter 1.7 (p. 47): 4 18.10.2007 Øving 8 Chapter 2.5: 3, 4, 6, 8, 11 (p.90-91) 25.10.07 Øving 9 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.] 01.11.07 Øving 10 Chapter 2.5: 7, 10, 15, 17 (p. 91-93) 08.11.07 Øving 11 Chapter 2.5: 13, 18, 19, 21 a, b, c (p. 92-94) 15.11.07 Øving 12 Chapter 6.7: 1, 2, 3 (p.312) 22.11.07 Øving 13 Chapter 3.5: 10, 11,12, 20 (p.147-149)

Treffetid:

Treffetid: Torsdag 11.15 - 12.00.

Lærebok:

Stein & Shakarchi: Real Analysis (Princeton Univ. Press, 2005)

Endelig pensum:

Chapters 1 (except Sect.5), Chapter 2 (except Sect.4), Chapter 3.3, Chapter 6.1 & 2.

Midtsemesterprøve:

Tirsdag 2.oktober, 12.15 – 14.00, F4

Eksamen:

4. desember 2007, 4 timer, skriftlig.

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