* The Final Exam will be "No Fault." See the
email I sent on Monday June 8 at 4:57 PM titled "140B Final Exam will
be No Fault" for details.
* During finals week, your TA will have office hours Tuesday 12:00 - 2:00 and will be available by appointment on Wednesday.
* During finals week, I will have office hours Wednesday 10:30 - 12:00 and 3:00 - 5:00.
* Your TA will have extra office hours for the exam Thurs. May 21 10:00 - 2:00 (same meeting ID as normal office hours)
* I will have extra office hours for the exam Thurs. May 21 2:00 - 4:00 (same Meeting ID as normal office hours)
* My office hours have changed again. For the rest of the quarter they will be W 10:30 - 12:00 and F 10:00 - 11:30.
* Your TA will have extra office hours for the exam Thurs. April 23 10:00 - 2:00 (same meeting ID as normal office hours)
* I will have extra office hours for the exam Thurs. April 23 4:00 - 6:00 pm via Zoom (same Meeting ID as normal office hours)
* Due to low activity on Piaza I have shifted all of my office hours to
be on Zoom (I will still respond to posts on Piazza though). My new
office hours are W 10:30-12, W 3-3:30, and F 10:15-11:15
Professor: Brandon Seward
(pronouns: he/him/his)
Lecture: MWF 1:00-1:50 via Zoom (navigate to
https://ucsd.zoom.us/j/878269867 or open the Zoom app and use Meeting ID 878-269-867)
Email: bseward@ucsd.edu
Office Hours via Zoom: W 10:30 - 12:00, F 10:00 - 11:30 AM (navigate to
https://ucsd.zoom.us/j/796484022 or open the Zoom app and use Meeting ID 796-484-022)
Note: Office hours and lecture have different Meeting IDs!
Teaching Assistant: Andres Rodriguez
(pronouns: he/him/his)
A01 Discussion: Mon. 4:00-4:50 via Zoom (navigate to
https://ucsd.zoom.us/j/613798086 or open the Zoom app and use Meeting ID 613-798-086)
A02 Discussion: Mon. 5:00-5:50 via Zoom (navigate to
https://ucsd.zoom.us/j/352538894 or open the Zoom app and use Meeting ID 352-538-894)
Email: a3rodrig@ucsd.edu
Office Hours via Zoom: Tu 12:00-2:00 and Th 10:00-12:00 (navigate to
https://ucsd.zoom.us/j/555398131 or open the Zoom app and use Meeting ID 555-398-131)
Website for Discussion: https://arodriguezrey12.wordpress.com/teaching/math-140b/
Course Descritption:
Second course in a rigorous three-quarter sequence on real analysis.
Topics include: differentiation, integration, sequences and series of
functions, some special functions.
Textbook: Principles of Mathematical Analysis by Walter Rudin, 3rd edition
. We will cover most of chapters 5 through 8.
Additional Study Materials: (you will not be tested on these)
- A list of errata in the course textbook (by George Bergman)
- A supplement to the exercises in the course textbook (by George Bergman)
- Elementary Analysis: The Theory of Calculus
by K. A. Ross, 2nd edition (standard textbook for 142A-B; less advanced
but may be helpful. Available for free to UCSD students on the campus
network, and can be found by searching in UCSD's Library Catalog).
- 140A-B Lecture Notes (by Todd
Kemp). Note that these lecture notes do not follow our textbook and may
cover slightly different topics. This is for reference only.
- The Devil's Staircase (by Todd
Kemp): a famous example of a monotone increasing function whose
derivative is 0 "almost everywhere" ("almost everywhere" is defined in
140C / Chap. 11 of Rudin).
- The Weierstrass Function (by Todd Kemp): a famous example of an everywhere continuous but nowhere differentiable function.
Lecture: Lecture will occur live on Zoom (use meeting ID: 878-269-867 or navigate to
https://ucsd.zoom.us/j/878269867). Videos of our lectures can be found on our Canvas page under the Media Gallery tab.
Lecture Notes PDF
Community Interaction:
Typically meeting in the classroom allows students the opportunity to
get to know one another and discuss the course material together. Since
class meetings will not occur, as a substitute we have a discussion
forum on Piazza that everyone is strongly encouraged to use. As part of
their weekly office hours, the professor and teaching assistant will
spend time each week responding to discussions on piazza (see above for
specific hours). Our piazza page is here:
http://piazza.com/ucsd/spring2020/math140b
Homework: Homework
will be assigned regularly and due on Fridays at 2:30. No late homework
will be accepted, but your lowest homework score will be dropped when
computing your final grade. On each assignment, a few problems will be
graded for correctness, while the others will be graded simply for
completion. We will use
Gradescope
for turning in homework. When registering for gradescope, please
register using your UCSD email address.
Homework 1 (Due Friday April 10):
Chapter 5 problems 2, 4, 6, 8, 9, 14, 19, 26 (Note: Convex function are
defined in exercise 23 on page 101 of the textbook)
Homework 2 (Due Friday April 17): Chapter 5 problems 11, 15, 17, 22 and Chapter 6 problems 1, 2, 3, 4
Homework 3 (Due Friday April 24): Chapter 6 problems 5, 7, 8
Homework 4 (Due Friday May 1): Chapter 6 problems 6, 10(abc), 11, 12, 13(abd), 15, 19 (Hint: Use problem 10 to solve two other problems)
Homework 5 (Due Friday May 8): Chapter 7 problems 1, 2, 3, 4, 8, 9, 14
Homework 6 (Due Friday May 15): Chapter 7 problems 7, 10, 13, 15, 16, 18, 19 (Note: Uniformly closed is defined in Definition 7.28. For #19, you can assume the truth of Ch. 2 problem 26)
Homework 7 (Due Friday May 22): Chapter 7 problems 20, 21, 23
Homework 8 (Due Friday May 29): Chapter 8 problems 1, 2, 4, 5, 6, 7,
9(a) (Note: These problems do not require any particular material from
chapter 8 aside from standard calculus identities for exponential,
logarithmic, and trigonometric functions.)
Homework 9 (Due Friday June
5): Chapter 8 problems 10, 11, 12, 13, 14, 22 (Only prove Newton's
binomial theorem), 23 (Note: Theorems 8.14 and 8.16(85) will be useful
for problems 12-14)
Exams:
The midterm exams will be taken at home and solutions will be uploaded
to Gradescope. The exams will be open-book and open-note, but the use
of online resources and help from other humans is forbidden. If
cheating is suspected, students will be required to have a one-on-one
zoom meeting where students will have to solve similar problems and/or
comment on their exam solutions.
Grading: The grading scheme has been updated. See the email I sent on Monday June 8 at 4:57PM titled "140B Final Exam will be No Fault."
Below is a record of the originally planned grading scheme:
Your final grade will be the maximum of the following two weighted averages:
- 20% Homework, 20% First Midterm, 20% Second Midterm, 40% Final Exam.
- 20% Homework, 20% Best Midterm, 60% Final Exam
Special Accommodations:
Students requiring accommodations should provide an OSD letter of
certification and OSD accommodation recommendation to the instructor as
soon as possible.
Course Schedule (items in gray may change)
Week
|
Monday
|
Wednesday
|
Friday
|
1 |
March 30
The derivative of a real function
|
April 1
The derivative of a real function
Mean value theorems
|
April 3
Mean value theorems
The continuity of derivatives
|
2 |
April 6
L'Hospital's rule
Derivatives of higher order
Taylor's theorem
|
April 8
Differentiation of vector-valued functions
|
April 10 - HW 1 Due
Definition and existence of the integral
|
3 |
April 13
Definition and existence of the integral
|
April 15
Definition and existence of the integral
|
April 17 - HW 2 Due
Definition and existence of the integral
Properties of the integral
|
4 |
April 20
Properties of the integral
|
April 22
Properties of the integral
Integration and differentiation
|
April 24 - HW 3 Due First Midterm (Solutions)
Practice Exam A Practice Exam B
Solutions A Solutions B
|
5 |
April 27 Integration and differentiation
Integration of vector-valued functions
Rectifiable curves
|
April 29
Discussion of main problem
Uniform convergence
|
May 1 - HW 4 Due
Uniform convergence
Uniform convergence and continuity
|
6 |
May 4
Uniform convergence and continuity
Uniform convergence and integration
Uniform convergence and differentiation
|
May 6
Uniform convergence and differentiation
Equicontinuous families of functions
|
May 8 - HW 5 Due
Equicontinuous families of functions
|
7 |
May 11
The Stone--Weierstrass theorem
|
May 13
The Stone--Weierstrass theorem
|
May 15 - HW 6 Due
The Stone--Weierstrass theorem
|
8 |
May 18
Power series
|
May 20
Power series
|
May 22 - HW 7 Due Second Midterm (Solutions)
Practice Exam A Practice Exam B
Solutions A Solutions B
|
9 |
May 25
Memorial Day
|
May 27
The exponential and logarithmic functions
The trigonometric functions
|
May 29 - HW 8 Due The trigonometric functions
The algebraic completeness of the complex field
Fourier Series
|
10 |
June 1
Fourier Series
|
June 3
Fourier Series
|
June 5 - HW 9 Due
Fourier Series
|
11
|
Thursday June 11, 11:30AM-2:30PM
Final Exam (Solutions)
Practice Final A, Practice Final B
Solutions A, Solutions B
|