Math 151A, Advanced Calculus I

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

Dr. Julie Bergner

 

Syllabus

 

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(d4 and d5 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

 

Julie Bergner’s web page

Last modified; 11 December 2008