Math 211: Multivariable Calculus

Instructor	Tanya Leise
Email	tleise at amherst dot edu
Phone	542-5411
Office	SMudd 503
Office hours	Mon 2:30-4pm Tues 10-11:30am Wed 2:30-4pm Thurs 2:30-4pm Other times by appointment or simply try stopping by my office
Q-Center help	Tim St. Onge is available Mon-Fri 11am-3pm in the Science Library
Math Fellows	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
Text	Stewart Multivariable Calculus 7E (on reserve in the science library, along with solutions manual)

Course goals

• 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 multivariable calculus
• Experience using Mathematica for graphing and computation
• Dare we say, have some fun doing mathematics?

Course Topics (Chapters 12-16)

• 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 several variables
• 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 effective 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 you missed and to get your assignments handed in to me.

Questions: If you have a question during lecture, please raise your hand and ask it right away. Chances are that other students are wondering the same thing. If a question arises later, feel free to visit my office and we'll work through sample problems until you are comfortable with the mathematics. Always feel free to ask me to slow down as well.

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 (30%).

Intellectual Responsibility

• 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:

1. 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 homework.
2. 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.
3. Each student must hand in his or her own problem set. You may not hand in a single packet as the work of multiple people. You must do your own write-up of each problem.
4. 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 yourself.
5. Be cautious in searching the web or other resouces for homework help. Copying solutions is plagiarism, whatever the source.
6. 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.

Homework Guidelines

• 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.

Exam Advice

• 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. 

Course Resources

Don't struggle alone! You have many options for getting help 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 numbered questions
• 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