Course information
Instructor: Prof. John Hunter
Lectures: MWF 9:00–9:50 a.m., Hart Hall 1150
Discussion sections:
MAT125AA01. Thur 9:00–9:50 a.m., Hutchison Hall 102
MAT125AA02. Thur 1:10–2:00 p.m., Hoagland Hall 113
Office hours: MWF 2:30–3:30 p.m.
CRN: 29189 (A01); 29190 (A02)
Office: MSB 2139
Office hours:
T 12:00–2:00 p.m.
W 12:00–1:00 p.m.
University of California
Davis, CA 95616, USA
email: jkhunter@ucdavis.edu
Office Phone: (530) 5541397
Office: Mathematical Sciences Building 3230
Announcement: Final
Final scores and course grades are posted on Smartsite. Solutions to the final are here.
Important Dates
 Instruction begins: Thu, Sep 27
 Last day to add: Fri, Oct 12
 Last day to drop: Wed, Oct 24
 Last class: Fri, Dec 7
 Academic holidays: Mon, Nov 12; ThuFri, Nov 2223
Exams
There will be two Midterms and a Final
 Midterm 1: Wednesday, Oct 24 (in class)
 Midterm 2: Wednesday, Nov 28 (in class)
 Final: Mon, Dec 10, 10:30 a.m.–12:30 p.m. (Exam Code B)
Grade
Grade will based on exams and homework, weighted
 10%: Homework
 25%: Each Midterm
 40%: Final
Text
Text: Elementary Real Analysis, Thompson, Bruckner, and Bruckner, Second Edition, 2008.
The text is available for free download from Clasical Real Analysis.
Syllabus and Notes
A syllabus and list of topics for the class is here.
Some class notes are here:
 Contents. Contents
 Chapter 1. Properties of R
 Chapter 2. Limits of Functions
 Chapter 3. Continuous Functions
 Chapter 4. Differentiable Functions
 Chapter 5. Sequences and Series of Functions
 Chapter 6. Power Series
 Chapter 7. Metric Spaces
A complete updated set of notes is here.
Midterm 1
Solutions to Midterm 1 are here.
A detailed list of the topics for Midterm 1 is here. Some practice midterm questions are here. Solutions to the practice midterm questions are here.
Midterm 2
Solutions to Midterm 2 are here.
A detailed list of the topics for Midterm 2 is here. Some practice midterm problems are here. Solutions to the practice problems are here.
Final
Solutions to the Final are here.
A detailed list of the topics for the Final is here. Some practice problems are here. Solutions to the practice problems are here. As always, do the problems yourself before you look at the solutions.
Homework
Homework will be assigned weekly and a hard copy will be due in class on Friday.
Please write clearly, or type, and staple your solutions.
If you want to type goodlooking mathematics, the standard tool is LaTeX, or one of its many variants,
and this would be as good a time as any to learn how to use it. See here
to get started.
Problem numbers refer to the exercises in the text.

Set 1 (Fri, Oct 5)
Sec 5.1.1, p. 182: 5.1.1, 5.1.11
Sec 5.1.2, p. 184: 5.1.16, 5.1.20
Sec 5.1.4, p. 187: 5.1.28
Sec 5.1.5, p. 189: 5.1.36
Sec 5.2.3, p. 194: 5.2.10, 5.2.16
Sec 5.2.4, p. 197: 5.2.17, 5.2.20
Sec 5.2.5, p. 199: 5.2.27
Read Sec 5.2 on "Properties of limits."Selected solutions on SmartSite are here.
Set 2 (Fri, Oct 12)
Sec 5.4.2, p. 212: 5.4.7, 5.4.13
Sec 5.4.3, p. 214: 5.4.17, 5.4.20
Sec 5.4.4, p. 217: 5.4.23, 5.4.24
Sec 5.5, p. 218: 5.5.2, 5.5.4
Sec 5.9.1, p. 225: 5.9.2, 5.9.6, 5.9.9
Sec 5.9.2, p. 229: 5.9.11, 5.9.12
Read Sec 5.9.1 on "Types of discontinuities" and Sec 5.9.2 on "Monotonic functions."Selected solutions on SmartSite are here.
Set 3 (Fri, Oct 19)
Sec 5.6, p. 221: 5.6.1, 5.6.3, 5.6.11
Sec 5.7, p. 223: 5.7.1, 5.7.2, 5.7.4, 5.7.6
Read the notes here that go over the definitions and properties of open, closed, and compact sets.Selected solutions on SmartSite are here.
Set 4 (Fri, Oct 26)
Sec 5.8, p. 224: 5.8.1, 5.8.2, 5.8.6, 5.8.9
Sec 4.2.4, p.151: 4.2.5
Sec 4.3.2, p.157: 4.3.5
Sec 4.5.5, p.171: 4.5.2, 4.5.6Selected solutions on SmartSite are here.
Set 5 (Fri, Nov 2)
Sec 7.2, p.274: 7.2.3 (a),(d), 7.2.5, 7.2.12, 7.2.15
Sec 7.2.2, p.276: 7.2.16
Sec 7.2.3, p.278: 7.2.26
Sec 7.3.1, p.280: 7.3.1, 7.3.4
Sec 7.3.2, p.284: 7.3.15
Sec 7.3.3, p.286: 7.3.18Selected solutions on SmartSite are here.
Set 6 (Fri, Nov 9)
Sec 7.5, p.291: 7.5.1, 7.5.2, 7.5.4
Sec 7.6.1, p.293: 7.6.1, 7.6.2, 7.6.4
(There's a typo in in 7.6.2: the equation should be x^3 + ax + b = 0.)
Sec 7.6.2, p.295: 7.6.8, 7.6.11, 7.6.13
Sec 7.7, p.299: 7.7.3, 7.7.4Selected solutions on SmartSite are here.
Set 7 (Fri, Nov 16)
Sec 7.12, p.322: 7.12.1, 7.12.5, 7.12.6 (You can assume l'Hospital's rule, Th. 7.42)
Sec 9.2, p.371: 9.2.1, 9.2.4, 9.2.7
Sec 9.3, p. 381: 9.3.1, 9.3.2, 9.3.3Selected solutions on SmartSite are here.
Set 8 (Fri, Nov 30)
Sec 9.3, p. 381 9.3.11, 9.3.13, 9.3.18, 9.3.20, 9.3.22
Sec 9.4, p. 386 9.4.1, 9.4.3, 9.4.10
Sec 9.6, p. 396 9.6.1, 9.6.2
Review material on series (Chapter 3 of the text), especially: Cauchy criterion; absolute convergence; comparison test; ratio test.Set 9 (Fri, Dec 7. Will not be collected.)
Sec 10.2, p. 408: 10.2.1
Sec 10.3 p. 411: 10.3.1
Sec 10.4 p. 417: 10.4.5
Sec 10.5 p. 423: 10.5.4
Sec 13.2 p. 541: 13.2.2, 13.2.10
Sec 13.4 p. 548: 13.4.7, 13.4.14 (a), (b), (c)
Sec 13.5 p.555: 13.5.9, 13.5.10
Sec 13.6 p. 562: 13.6.16
Some Extra Material
Plots of Some Functions. The function y = sin(1/x) and a detail near the origin. The function y = x sin(1/x) and a detail near the origin. The Thomae function, equal to zero for irrational numbers and 1/q for rational numbers p/q with p, q relatively prime, and a blowup for small yvalues
Definition of Continuity. If you find the εδ definition of continuity a bit unintuitive, you might like this article by Keith Devlin.