Math 151A, Advanced Calculus I

Fall 2008, TTh
2:10-3:30 pm, Sproul 2339

Dr. Julie Bergner

Thursday, September 25: Rational and irrational numbers, upper
and lower bounds

Homework: pg. 21
#1, 2, 4 (due Tuesday, September 30)

Tuesday, September 30: Least upper bound property, field axioms
and consequences

Homework: pg.
22 #3, 5 (due Tuesday, October 7)

Thursday, October 2: Construction and properties of real numbers

Homework: pg.
22 #6 (due Tuesday, October 7)

Tuesday, October 7: The extended real numbers, complex numbers,
and Euclidean spaces

Homework: pg 22, #8, 10, 12, 18 (due Tuesday, October 14);
corrections to last week’s assignment if you wish (due Thursday, October 9)

Thursday, October 9: Set theory review

Homework: pg.
43, #1, 4 (due Tuesday, October 14)

Tuesday, October 14: Metric spaces, open and closed sets, limit
points

Homework: pg.
43, #5, 7, 9, 11(d_{4} and d_{5} only) (due Tuesday, October
21); corrections to last week’s assignment of you wish (due Thursday, October
16)

Thursday, October 16: Compact spaces

Homework: pg 44, #12, 14 (due Tuesday, October 21)

Tuesday, October 21: Perfect sets and uncountability

Homework: pg.
44: #19, 22, 29 (due Tuesday, October 28); corrections to last week’s
assignment if you wish (due Thursday, October 23)

Thursday, October 23: Sequences

Homework: pg.
78 #1, 2 (due Tuesday, October 28) ***Note that #3 has been deferred
until next week.***

Tuesday, October 28: Cauchy sequences

Homework: pg.
82 # 20, 23 (due Tuesday, November 4); corrections to last week’s assignment of
you wish (due Thursday, October 30)

Thursday, October 30: Subsequential
limits

Homework: pg.
78 #3, 4, 21 (due Tuesday, November 4)

Tuesday, November 4: Midterm exam

(Covering
chapters 1, 2, and the first part of chapter 3, on sequences)

Homework:
Corrections to last week’s assignment if you wish (due Thursday, November 6)

Thursday, November 6: Series

Homework:
Corrections to midterm exam (due Thursday, November 13)

Tuesday, November 11: Veteran’s Day – no class

Thursday, November 13: Root test, ratio test, and power series

Homework: pg.
78 #6, 7, 19 (due Tuesday, November 18); corrections to last week’s assignment
if you wish (due Thursday, November 20)

**Note office hours have been changed to Monday and Wednesday
2-3 pm**

Tuesday, November 18: Power series and absolute convergence

Homework: pg.
79: #8, 9, 10, 13 (due Tuesday, November 25)

Thursday, November 20: Rearrangements of series, and limits of
functions

Homework: pg.
98 #1 (due Tuesday, November 25)

Tuesday, November 25: Properties of continuous functions

Homework: pg.
98 #2, 3, 4 (due Tuesday, December 2); corrections to last week’s assignment if
you wish (due Thursday, December 4)

Thursday, November 27: Thanksgiving – no class

Tuesday, December 2: Continuous functions on compact spaces,
uniform continuity

Homework:
corrections to last week’s assignment if you wish (due Thursday, December 4)

Thursday, December 4: Properties of continuous functions,
discontinuities, limits at infinity

Suggested
problems from this week’s material: pg. pg. 99 #8, 9, 10, 11 (don’t worry about
application to 13), 14, 15, 16

(You may turn
these in if you would like feedback before the final. They are not required homework, but strongly
recommended.)

Solutions to
them can be found here.

Final exam: Friday, December 12, 8-11 am, in the usual classroom

Last
modified; 11 December 2008