Homework for Elementary Analysis
Math 315, Spring 2017, University of Oregon
Max Kutler
All exercises are taken from the 2nd edition of Abbott.
To use the .tex files below, you will need to download hmcpcet.cls
from https://www.math.hmc.edu/computing/support/tex/classes/hmcpset/. If
you need help installing the .cls file, please ask!
1. Due Friday, 4/7: Preliminaries
2. Due Tuesday, 4/11: Consequences of completeness
Reading: 1.4-1.6
Homework: 1.3.5, 1.3.8, 1.4.1, 1.4.3
tex, pdf
3. Due Friday, 4/14: Cardinality and sequences
Reading: 2.1-2.2
Homework: 1.4.5, 1.5.9
tex, pdf
4. Due Tuesday, 4/18: Limits
Reading: 2.2
Homework: 2.2.2, 2.2.3, 2.2.5, 2.2.6
tex, pdf
5. Due Friday, 4/21: The algebraic and order limit theorems
Reading: 2.3
Homework: 2.3.1, 2.3.9
tex, pdf
Rewrite: Homework 1
6. Due Tuesday, 4/25: The monotone convergence theorem
Reading: 2.4
Homework: 2.3.7, 2.4.1, 2.4.2, 2.4.3
tex, pdf
Rewrite: Homework 2
7. Due Friday, 4/28: Subsequences and Bolzano-Weierstrass
Reading: 2.5
Homework: 2.5.5, 2.5.7
tex, pdf
Rewrite: Homework 3
8. Due Friday, 5/5: The Cauchy criterion and infinite series
Reading: 2.6-2.7, 2.9
Homework: 2.6.4, 2.7.7, 2.7.9
tex, pdf
Rewrite: Homework 4
9. Due Tuesday, 5/9: Basic topology
Reading: 3.1-3.2
Homework: 3.2.1, 3.2.3, 3.2.4, 3.2.7
tex, pdf
Rewrite: Homework 5 & Homework 6
10. Due Friday, 5/12: Compactness
Reading: 3.3
Homework: 3.3.2, 3.3.4 (Extra Credit: 3.3.7)
tex, pdf
Rewrite: Homework 7
11. Due Tuesday, 5/16: Connectedness
Reading: 3.4 (subsection on perfect sets is optional)
Homework: Problem A, 3.4.5, 3.4.7
tex, pdf
12. Due Friday, 5/19: Functional limits
Reading: 4.1-4.2
Homework: 4.2.7, 4.2.8
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Rewrite: Homework 8
13. Due Tuesday, 5/23: Continuity
Reading: 4.3-4.5
Homework: 4.3.1, 4.3.9, 4.4.3, 4.4.9
tex, pdf
Rewrite: Homework 9
14. Due Wednesday, 5/31: IVT and derivatives
Reading: 5.1-5.2
Homework: 4.5.3, 4.5.7, 5.2.7, 5.2.10
tex, pdf
Rewrite: Homework 10
15. Due Friday, 6/2: MVT
Reading: 5.3-5.4
Homework: 5.3.7, 5.3.8
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Rewrite: Homework 11 & Homework 12
16. Due Tuesday, 6/6: Sequences of functions
Reading: 6.1-6.2
Homework: 6.2.1, 6.2.3 (Extra Credit: 6.2.12)
tex, pdf
Rewrite: Homework 13
17. Due Friday, 6/9: Uniform convergence and differentiation; series
of functions
Reading: 6.3-6.4
Homework: 6.3.1, 6.4.3
tex, pdf