Math 621 Fall 2012 Homework

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Homework is due on fridays in lecture (unless noted otherwise).

Do check the homework page periodically for new homework or changed homework. Hitting the "Reload" or "Refresh" button on your browser with Ctrl or Shift pressed down (depends on the browser) usually makes absolutely sure that you have the newest version.

Homework is from Spivak unless otherwise noted.

Homework 1 (due Friday Sep. 14)

page 4) 1-1, 1-6, 1-7, 1-10
page 10) 1-16, 1-17, 1-22
page 13) 1-25, 1-29

Homework 2 (due Friday Sep. 21)

page 17) 2-1, 2-4, 2-5, 2-7, 2-8
page 22) 2-10 h, 2-12, 2-16
page 28) 2-21, 2-22

Homework 3 (due Friday Sep. 28)

page 28) 2-23, 2-25, 2-26 (it may seem like an arbitrary construction, but the functions defined here are incredibly important in making local proofs into global ones, and especially useful once we get to manifolds)
page 33) 2-28 a, 2-29, 2-31, 2-34 (this is Euler's homogeneous function theorem)
page 39) 2-36

Homework 4 (due Friday Oct. 5)

page 39) 2-38, 2-39
page 43) 2-41
page 49) 3-1, 3-2, 3-3, 3-5, 3-6, 3-7

Homework 5 (due Friday Oct. 12)

page 52) 3-10, 3-12, 3-13
page 56) 3-14, 3-15, 3-16, 3-17, 3-22

Homework 6 (due Friday Oct. 26)

I recommend looking even at the unassigned problems, since this homework skims more due to 2 weeks of material being covered.

page 61) 3-27, 3-28, 3-32, 3-34, 3-35
page 66) 3-37, 3-38 (these problems show the subtlety of the concept of integrability, in 3-38 be careful to note what is it that converges absolutely, and note that we require a stronger statement for integration in the extended sense)
page 72) 3-39

Homework 7 (due Friday Nov. 2)

page 61) 3-26
page 72) 3-40, 3-41
page 84) 4-1, 4-2

Homework 8 (due Friday Nov. 9)

page 85) 4-3, 4-5 (the square brackets denote orientation), 4-6, 4-7, 4-9, 4-12
page 96) 4-13, 4-14

Homework 9 (due Friday Nov. 16)

page 96) 4-16, 4-18, 4-19, 4-20, 4-21
page 100) 4-23, 4-24

Homework 10 (due Monday Nov. 26)

page 104) 4-25, 4-26, 4-27, 4-28, 4-29, 4-32
page 114) 5-1, 5-2

Homework 11 (due Friday Nov. 30)

page 114) 5-3, 5-4, 5-5, 5-6, 5-8 (in b by boundary of M he means topological boundary)

Homework 12 (due Friday Dec. 7)

page 121) 5-10, 5-11, 5-12, 5-15, 5-16, (optionally try 5-14 and 5-17)

Homework 13 (not due)

Of course you should try all of the problems, I'm just recommending that you really try these.

page 125) 5-18, 5-19, 5-20
page 130) 5-23, 5-24, 5-25, 5-27, 5-29
page 137) 5-34, 5-36