Course information
Instructor: Prof. John Hunter
Lectures: MWF 9:00–9:50 a.m., Olson 106
Office hours: M 1:30–2:30 p.m.; W 2:30–3:30 p.m.
Discussion sections:
A01 (CRN 48977): Tue 9:00–9:50 a.m., Olson 106
A02 (CRN 63561): Tue 9:00–9:50 a.m., Physics 130
David Stein (Office: MSB 2125)
Matthew Cha (Office: MSB 2129)
Office hours
David Stein: TR 12:00–1:00 p.m.
Matthew Cha: M 12:00–1:00 p.m., T 2:00–3:00 p.m.
University of California
Davis, CA 95616, USA
email: jkhunter@ucdavis.edu
Office Phone: (530) 5541397
Office: Mathematical Sciences Building 3230
Final Exam
Final exam solutions are here.
Important Dates
 Instruction begins: Mon, Apr 1
 Last day to add: Tue, Apr 16
 Last day to drop: Fri, Apr 26
 Last class: Wed, Jun 5
 Academic holiday: Mon, May 27
Exams
There will be two Midterms and a Final
 Midterm 1: Wed, Apr 24 (in class)
 Midterm 2: Wed, May 22 (in class)
 Final: Tue, June 11, 3:30 –5:30 p.m. (Exam Code N: in 66 Roessler)
Grade
Grade will based on exams and homework, weighted
 10%: Homework
 25%: Each Midterm
 40%: Final
Text
Text: Foundations of Analysis, Joseph L. Taylor, 2012.
Syllabus
A syllabus for the class is here.
Notes
Some class notes are here:
A set of lecture notes for MAT 125B written by Steve Shkoller is here.
Midterm 1
Midterm 1 covers Sections 5.15.3 of the text on the definition, existence and properties on the Riemann integral and the fundamental theorem of calculus. The exam will be closed book, so you should know the precise statements of the theorems in the text and homework problems.
Solutions to Midterm 1 are here.
Midterm 2
Solutions to Midterm 2 are here. Midterm 2 covers material from Sections 7.17.3, 8.1, and 9.19.4 (up to p. 245) on the text:
 7.1 Euclidean space
 7.2 Norms and convergence in R^{n}
 7.3 Open and closed sets
 8.1 Continuous functions in R^{n}
 9.1 Partial derivatives
 9.2 The differential
 9.3 The chain rule
 9.4 Directional derivatives, gradients, and tangent vectors
The emphasis will be on the differential calculus in 9.19.4, with background material from 7.17.3 and 8.1 as needed.
The exam won't be closed book. You're allowed to prepare an 8 1/2 x 11 inch "cheat sheet" (front and back) and use it during the midterm, but no other references are permitted.
Some sample Midterm problems are here. You don't need to turn them in with the Homework problems. (I corrected a typo in Problem 5.)
Solutions to the sample Midterm problems are here. I strongly recommend that you try the problems yourself before you look at the solutions!
Some solutions to selected homework problems in Chapter 9 are here.
Final Exam
 The final exam will be Tuesday, June 11, 3:305:30 p.m.
 It will be in 66 Roessler Hall, not our regular classroom.
 The final will be comprehensive and include all the material we've covered in class.
 You're allowed to prepare an 8 1/2 x 11 inch "cheat sheet" (front and back) and use it during the final, but no other references are permitted.

I'll hold final's week office hours on Monday, June 10, 2:30 p.m.  4:00 p.m.
 5.1 Definition of the integral
 5.2 Existence and properties of the integral
 5.3 The fundamental theorem of calculus
 5.4 Improper integrals
 7.1 Euclidean space
 7.2 Norms and convergence in R^{n}
 7.3 Open and closed sets
 8.1 Continuous functions in R^{n}
 9.1 Partial derivatives
 9.2 The differential
 9.3 The chain rule
 9.4 Directional derivatives, gradients, and tangent vectors
 9.6 The inverse function theorem
 10.1 Integration over a rectangle
 10.210.3 Integration over Jordan regions
 10.4 Iterated integrals
 10.5 Change of variables
Here's a detailed list of the sections in the text that we've covered.
For practice, here's a previous Math 125B final, which was taught by another Professor. (There aren't any multivariable integration questions, and Problems 4 and 6 are a little outside the material we discussed, but you should still be able to do them.)
Homework
Homework will be assigned weekly and a hard copy will be due in class on Wednesdays. Please write clearly or type, give logical easy to follow proofs, and staple your solutions.
If you want to type goodlooking mathematics, the standard tool is LaTeX, or one of its many variants. See here to get started.
Problem numbers refer to the exercises in the text.
Set 1 (Wed, Apr 10)
Sec 5.1, p. 107: 2, 3, 8, 11
In case you don't have the text yet, a copy of the Exercise Sets is
here.
Set 2 (Wed, Apr 17)
Sec 5.2, p. 113: 1, 2, 6, 8, 9, 11, 14
Sec 5.3, p. 119: 4, 5, 6, 9, 10, 12
In case you don't have the text yet, a copy of Set 5.3 is
here
and here.
Some solutions are in the lecture notes.
 5.2.2: Proposition 1.39
 5.2.8: Theorem 1.31 and Proposition 2.19
 5.2.9: Theorem 1.26
 5.2.14: Example 1.40
 5.3.9: Proposition 1.35
Set 3 (Wed, Apr 24)
Problem set 3 is
here.
It includes a number of sample midterm problems which you should turn in as part of the homework.
Some solutions are in the lecture notes.
 5.2.10: Theorem 1.26
 Sample question 1: Example 1.57
Set 4 (Wed, May 1)
Sec 5.4, p. 127: 9, 10, 12, 15
Two additional problems on uniform convergence, which are: here
A copy of the problems is Sec 5.4 is
here
Some solutions are in the lecture notes.
 5.4.9: Example 1.70
 5.4.10: Example 1.68
 Additional question 2: Theorem 1.64
Set 5 (Wed, May 8)
Sec 7.1, p.167: 5, 8, 9
Sec 7.2, p.173: 1, 8, 10
Sec 7.3, p.178: 1, 4, 5, 8
Read over Chapters 7 and 8 in the text.
A copy of the problem sets is
here
Set 6 (Wed, May 15)
Sec 9.1, p.228: 1, 6, 8, 10
Sec 9.2, p. 235: 1, 2, 3, 4, 8, 9, 10, 11
Set 7 (Wed, May 22)
Sec 9.3, p. 241: 2, 4, 8, 10
Sec 9.4, p. 250: 1, 2, 3, 6
Set 8 (Wed, May 29)
Sec 9.6, p. 265: 1, 2, 4, 10, 11
The additional problem
here
A solution to Problem 9.6.11 on representing a parametric curve by Cartesian equations is
here.
Set 9 (Wed, June 5)
Sec 10.1, p. 282: 3, 4, 10
Sec 10.2, p. 287: 3, 4
Sec 10.4, p : 2, 4
Sec 10.5, p. : 3, 4, 7