Math 31BH Winter 2023
For everyone's health, please wear masks in class and office hours
Professor
Elham Izadi ; AP&M 6240 ; 858-534-2638 ;
eizadi@math.ucsd.edu ; Office hours in AP&M 5829: 14:00-15:00 Tuesdays and Thursdays ;
Exceptionally, on Tuesday February 28th, office hours will be 15:00-16:00 (room 5829 as usual)
Lectures: Tuesday, Thursday 11:00-12:20 AP&M B402A
Final Exam: 03/23/2023 11:30-14:29, room B402A
Teaching Assistant
Shubham Saha ; HSS 4005 ; shsaha@ucsd.edu ; Office
hours: 15:00-17:00 Mondays
Discussion Sections: Wednesdays 17:00-17:50 and 18:00-18:50 AP&M 2301
Course description
Second quarter of three-quarter honors
integrated linear algebra/multivariable calculus sequence for
well-prepared students. Topics include derivatives in several
variables, Jacobian matrices, extrema and constrained extrema. (Credit
not offered for both MATH 31BH and 20C.)
The Honors Calculus sequence is: 31AH, 31BH (Honors Multivariable
Calculus), 31CH (Honors Vector Calculus). These are very roughly equivalent to Math 18,
20C, and 20E respectively, but far more sophisticated and
rigorous. Because of the heavy emphasis on proof in this sequence,
students completing it will be exempt from taking Math 109
(Mathematical Reasoning).
Prerequisites
MATH 31AH with a grade of B- or better, or consent of instructor.
Text
Vector Calculus, Linear Algebra, and Differential
Forms, A Unified Approach; by John Hamal Hubbard and Barbara Burke
Hubbard. Fifth Edition.
Many of the marginal notes in the textbook are distracting, but
some are important, so please don't overlook them. On the publisher's
web site Matrix Editions you will
find a list of typos in the book. Last quarter you covered Sections
0.1-0.4, 1.1-1.4 and 2.1-2.7. This quarter we will cover Sections
1.5-1.9, 2.10, 3.1-3.4, 3.6-3.7.
Homework
There will be weekly homework assignments, posted on this web site on Wednesdays.
You are encouraged to work on these problem sets with a
small group of other students in the class, but every student should
write up his or her own solutions. Homework solutions should be easily
readable and include clear explanations in words and diagrams of your
reasoning, not merely a string of equations. The problems are very
challenging: you should start working on them as soon as you are
able so you have ample time to ask for help if needed. Another
reason is that it is often beneficial to think about a problem several
times on different days: your brain continues to process the
problem more or less continuously from the time
you first look at it.
Weekly homework will be due on Wednesday before 23:59 (midnight). Please upload a
pdf file of your homework to Gradescope (which you can access through Canvas).
No late homework will be accepted. However, the lowest homework grade
will be dropped.
Reading
Please make sure to fully and very carefully read the sections
of the textbook corresponding to the assigned homework exercises;
there will be some questions on the exams on the assigned reading
whether or not it is discussed in the lecture (please ask me or your
TA for help with the assigned reading if you need help).
Exams
Final Exam: Thursday March 23rd, 11:30-14:29, in
B402A. As usual, the final exam is cumulative.
Midterm 1: Thursday February 2nd, in class
Midterm 2: Thursday March 2nd, in class
No make-up exams will be given (please see the grading policy
below in case you miss a midterm). No textbooks, notes,
calculators, phones or electronic devices are allowed during
exams.
You do not need to bring anything other than a pen or
pencil to the exam. We will not use blue books.
Please ensure that you do not have a schedule conflict involving
the final examination; you should not enroll in this class if you
cannot take the final examination at its scheduled time.
Grading
Your final grade for the course will be the maximum of the following
Homework: 20%, Each midterm: 20%, Final: 40%
Homework: 20%, Midterm 1: 20%, Final: 60%
Homework: 20%, Midterm 2: 20%, Final: 60%
In addition, you must pass the Final Exam in order to pass the course.
Since there are no makeup exams, if you miss a midterm then your
course grade will be computed with your final exam counting 60%.
Regrade Requests
You midterm exams will be returned to you in
discussion section. If you wish to have the grader take a second look at
your exam, please attach a note explaining your concern and
return the exam to your TA. Regrade requests will not be
considered once your exam leaves the room.
Academic Honesty and Integrity
UCSD's code of academic integrity
outlines the expected academic honesty of all students and faculty,
and details the consequences for academic dishonesty. The main issues
are cheating and plagiarism. However, academic integrity also includes
things like giving credit where credit is due (listing your
collaborators on homework assignments, noting books, webpages, or
other resources containing information you used in solutions, etc.).
Helpful advice
The material in this course is complex and
challenging, emphasizing proofs of all the key theorems as well as
computational methods. Read each section in the textbook carefully
before we cover it in class (please see below for the section of the
book we will cover in each lecture). Don't expect to understand
everything, but bring questions to class. The terminology, facts, and
methods we develop will all be used in the rest of the 31H
sequence. Be sure you know and understand the definitions and
applications of basic concepts. Because each concept builds on those
preceding it, it is important not to fall behind. Ask questions right
away in class, in section, or at office hours if you feel unsure about
any concept we cover; do not try to catch up the night before the
exam!
Sections of the book to read before we cover them:
For January 12 and 17: read Section 1.5
For January 19: read Section 1.6 (skip the fundamental theorem of algebra)
For January 24: read Section 1.6, 1.7
For January 26: read Section 1.7
For February 7: read Section 1.7
For February 9: read Section 1.9
For February 14: read Sections 1.8, 1.9
For February 21: read Sections 3.1, 3.2
For February 23: read Section 2.10
For March 7: read Section 3.3
For March 9: read Section 3.4, 3.6
For March 14: read Sections 3.6, 3.7
Some class notes:
01/10/2023
01/12/2023
01/17/2023
01/19/2023
01/24/2023
01/26/2023
01/31/2023
02/07/2023
02/09/2023
02/14/2023
02/16/2023
02/21/2023
02/23/2023
02/28/2023
03/07/2023
03/09/2023
03/14/2023
03/16/2023
Homework assignments:
Homework 1: due Wednesday January 18
1.5.1, 1.5.2, 1.5.3, 1.5.4, 1.5.7, 1.5.14, 1.5.19, 1.5.20 Solutions
Homework 2: due Wednesday January 25
1.5.10, 1.5.11, 1.5.12, 1.5.13, 1.6.6, 1.6.7 (hint for 1.6.7: use the function g(x) = f(x)-mx) and these problems Solutions
Homework 3: due Wednesday February 8
1.6.2, 1.7.2, 1.7.4, 1.7.5, 1.7.6, 1.7.7, 1.7.11, and these problems Solutions
Homework 4: due Wednesday February 15
1.7.10, 1.7.14, 1.7.15, 1.7.21, 1.9.1, 1.9.2 and 1.28, 1.32 from the review exercises (for problem 1.7.10(b), prove the contraposite: if f satisfies the equality, then f is affine)
The following product rule for functions of matrices is useful for some of the exercises. Solutions
Homework 5: due Wednesday February 22
1.8.2, 1.8.5, 1.8.8, 1.8.10(a), 1.8.12, 1.8.13, 1.7 from the review exercises and the following exercise. Solutions
Homework 6: due Wednesday March 8
2.10.1, 2.10.6, 2.10.9, 3.1.8(a)(b), 3.1.11, 3.1.12, 3.2.6 and the following exercise.
(for 3.1.11, the surface X is the union of the lines through the origin and the point (t, t2, t3) where t is nonzero: X does not contain the origin) Solutions
Homework 7: due Friday March 17
3.3.6 (Similarly, what can you say about functions that satisfy $f(x) = f(-x)$?), 3.3.9, 3.3.11, 3.4.1, 3.6.1, 3.6.2, 3.6.7 and the following exercise. Solutions
Homework 8: due Wednesday March 22
3.7.3(a), 3.7.4(a), 3.7.6, 3.7.7(a), 3.7.13, 3.7.15, 3.7.16 and 3.20(a) from the review exercises for Chapter 3. Solutions