Math 211: Multivariable Calculus
||tleise at amherst dot edu
Other times by appointment or simply try stopping by my office
||Tim St. Onge is available Mon-Fri 11am-3pm in the Science Library
||All evening hours are in Seeley Mudd 205:
Sunday 6:00 – 8:00 pm Amos (Zeus) Tuwei
Sunday 8:00 – 10:00 pm Michael Bakshandeh
Monday 7:00 – 9:00 pm Michael Bakshandeh
Tuesday 8:00 – 10:00 pm Amos (Zeus) Tuwei
Wednesday 8:00 – 10:00 pm Liubou (Yuuna) Klindziuk
Thursday 8:00 – 10:00 pm Liubou (Yuuna) Klindziuk
Stewart Multivariable Calculus 7E
(on reserve in the science library, along with solutions manual)
- Become proficient in analyzing
functions of several variables
and vector functions
- Understand and write basic proofs involving
essential concepts in calculus
- Learn some applications of
- Experience using Mathematica for graphing and computation
- Dare we say, have some fun doing
Course Topics (Chapters
- Elementary vector analysis, including
dot and cross products, lines and planes, tangent and normal vectors,
velocity and acceleration
- Limits, continuity, and
differentiation of functions of several variables
- Directional derivative and gradient;
tangent plane to a surface
- Maxima and minima of functions of
- Double and triple integrals, including
cylindrical and spherical coordinates
- Line integrals and Green's Theorem
- Surface integrals, Stokes' Theorem, and Divergence Theorem
Attendance: You are
to be in class and to be there on time. Cooperative learning is more
and more fun than struggling through material on your own.
If you do
miss a lecture, it is your responsibility to obtain the material that
missed and to get your assignments handed in to me.
have a question during lecture, please raise your hand and ask it right
Chances are that other students are wondering the same thing. If a
arises later, feel free to visit my office and we'll work through
problems until you are comfortable with the mathematics.
Always feel free to ask me to slow down
Grading: Your course grade will be based on
three in-class exams (best two exams 20% each, 10% for the third), homework (20%), and the final exam
- Exams. Your work must be entirely your own, so
please follow the guidelines of the honor code. Unless I explicitly
allow other aids, you are only allowed whatever implements you need to
read and write (no notes or calculators). Turn off your
cell phone to avoid inadvertently distracting your fellow test-takers and to follow the honor code. Clocks are available in the classrooms, so cell phones and all other electronic devices are not needed and must be turned off during exams.
Use of a cell phone or any other electronic device during an exam (unless it is an emergency) may be grounds for receiving an F on that exam.
- Homework. I encourage you to study with other students and form study groups to work regularly together. Going to the Q-Center drop-in hours for Math 211 can be a good way to find others to study with, plus you have help right on hand to answer your questions. To ensure your study is effective,
follow these guidelines:
- If you worked with or received help
from any source other than me, you should put a note on the front of
your homework saying, "I worked with <names>."
Make sure your name stands out as the author of your
- Working together does not mean that
one of you does the first half of the homework set and the other does
the second. Everyone should work on every problem.
- Each student must hand in his or her
own problem set. You may not hand in a single packet as the work of
You must do your own write-up of each problem.
- Do not copy someone else's
solution—you will not learn anything and it is plagiarism. Discuss problems with others, and then you must be
able to work out the solution on your own again and write it down
- Be cautious in searching the web or other resouces for homework help. Copying solutions is plagiarism, whatever the source.
- If you are unsure what agrees or
does not agree with the precepts of intellectual responsibility in this
course, feel free to talk to me about it.
- All problem sets are due at THE
START OF CLASS.
Late homework will receive half credit for homework handed
in after start of class but by the start of the next class meeting (and will not accepted after
that, unless you contacted me in advance to obtain an extension).
- If you are unable to attend class due
to illness or an emergency, let me know as soon as you can and we will
work out an appropriate schedule for assignments.
- Your name should be written on all
sheets, in case pages get separated.
- Multiple pages must be STAPLED.
- Homework should be neat. Please no messy edges
from notebook paper.
- Where appropriate, please box or
highlight final answers. Answers should be in the right order and easy to find and read.
Keep the grader happy!
- As mentioned elsewhere, no copying!
Always keep the honor code in mind to maintain an ethical environment in which everyone truly learns the material.
- Organize important definitions, theorems, and methods into a sheet and make sure you have them memorized. Start preparing and memorizing the items on your summary sheet well in advance of the exam so you have them in long-term memory (and not just short-term memory, which is less reliable under exam pressure). Adding items to your summary sheet as we go through the material and regularly reviewing it can be a very effective strategy in any math class.
- After reviewing the material and working some review problems, take the practice exam under exam-like conditions, without using notes or the textbook, and in the same room, if possible, as the exam itself. Memory recall can be strongest when you are physically in the same location as where you learned it or used it, and taking exams has been found to increase performance on the next similar exam. So use these facts to your advantage!
- Be aware of psychological influences like stereotype threat. If you think about reasons you won't do well or even about negative stereotypes that may apply to you, your exam performance can be detrimentally affected. Instead spend the ten minutes before an exam reviewing your past successes with math or other exams. Write down your concerns and thoughts, and then jot down a few positive reasons for why you will nail this exam.
- Mentally go through some of the important ideas and methods to warm up your "math muscles" and focus your thinking as you wait to begin the exam.
- These strategies can prime your brain for optimal performance on the exam, and they're well worth giving a try.
Inclusion and Accessibility
I strive to make all my courses welcoming to all students. I am happy to discuss your learning needs and strategies to best support your academic success. If you have a documented disability that requires accommodations, please register with Accessibility Services at the college, and contact me to let me know what accommodations you will need for this course. Whenever possible, please give me at least two weeks advance notice to implement these accommodations.
Don't struggle alone! You have many options for
with this course.
- Me. Feel free to come to my office hours,
make an appointment by email or phone, or simply try stopping by my
office—you are welcome whenever my door is open. If
you have some anxiety about taking math exams, please come see me and
we can work together on building your math confidence.
- Homework. Although the practice problems are not
graded, please work through them. Mathematics
is learned ACTIVELY, not passively. You
can't absorb math through listening or reading, even if you think you
understand it all.
- Textbook. I won't go over everything that is
contained in the text, and I try to avoid doing the same examples. Hence your textbook in an important
independent source of information and you should read it!
- Lecture notes. Reviewing the notes you take in lecture
will give you a chance to see the material again after you have had
some time to assimilate it.
- Your classmates. Discussing math with others can help you
think through the concepts. Explaining an
idea you already understand will deepen your comprehension, and for the
concepts that you don't understand well, the explanation of a peer may
be more helpful than mine or the textbook's.
- The QCenter. The Quantitative Skills Center provides drop-in help afternoons and evening,
as well as some one-on-one tutoring.
- Math Fellows. Michael Bakshandeh, Yuuna Klindziuk and Zeus Tuwei will hold regular evening drop-in hours where you can get help and find other Math 211 students to study with.
- Library resources. The following Stewart/related books are
on reserve in the Science Center:
- Single Variable Calculus
- Multivariable Calculus
- Student solutions manuals for the
single variable text
- Student solutions manual for the
multivariable text, containing somewhat detailed answers to the odd
- Mathematica can be helpful for graphing of surfaces
and double-checking calculations like integrals, and we will be using it regularly in class. Mathematica is available for all
college-owned computers, and is already installed in all of the public
labs, e.g. in on the first floor of Seeley Mudd. Mathematica
can be installed on your own computer (https://www.amherst.edu/offices/it/knowledge_base/software/college-install) or accessed through a Remote Desktop Connection (https://www.amherst.edu/offices/it/knowledge_base/network-wifi/Remote_Desktop_Connection).
To the Math 211 Homework Schedule