There is also a web page on Courseworks. These sections use WebAssign.

Time: MW 1:10-2:25 p.m. (Section 002) and MW 2:40-3:55 (Section 003)
Place: Math 207
Textbook: Calculus: Early Transcendentals (seventh edition) by James Stewart.
Office hours: M 4:15-6:15 p.m., W 9:00-10:00 a.m. in Math 625.
Teaching assistants: Paul Lewis, Zhuhai Wang, Alex Phu Dang, Yubo Han, Yih-Jen Ku, Tomer Mate
Help room hours: T 12:00 - 3:00 (Wang), Th 12:00-3:00 (Lewis), F 10:00-12:00 (Han), W 2:00-4:00 (Ku), F 2:00-4:00 (Mate), T 3:00-6:00 (Dang, in Math 406)
Final exam dates:

• Section 2: Monday, May 11, 1:10 - 4:00 p.m.
• Section 3: Wednesday, May 13, 1:10 - 4:00 p.m.

Syllabus Problem sets Handouts Policies Advice

## Prerequisites.

Calculus I or equivalent is required, though Calculus II or equivalent is recommended. See this web page for more details about which calculus class is appropriate for you.

## Description and goals.

Math V1201 extends techniques from differential calculus to functions of several variables. The main goals are:

• To develop techniques for solving higher-dimensional problems occuring throughout science and engineering. There is a particular focus on maximization / optimisation of functions subject to constraints.
• To develop a geometric language for talking about higher-dimensional spaces, with a particular emphasis on two- and three-dimensions.
• To develop a geometric intuition about vectors in two- and three-dimensions necessary for the more general study of vector spaces in linear algebra (Math V2010).
• To review a few other fundamental mathematical tools (notably, the complex numbers) central to the sciences and engineering.

In the process, the course covers a substantial amount of beautiful mathematics. Many simple phenomena in one dimension (e.g., continuity) become much more subtle -- and interesting -- in higher dimensions. Other phenomena (e.g., linear approximation) become clearer in the context of functions of several variables.

## Policies.

 Online Homework 15% Written Homework 10% Midterm 1 20% Midterm 2 20% Final exam 35%

The lowest two online homework scores and the lowest two written homework scores will be dropped. Because of the size of the class, late homework will not be accepted.

### Homework

Online homework, via WebAssign, is due online before class starts. WebAssign homework will typically be due twice a week. In addition, written homework will be due at the beginning of class on Mondays. If you can't make it to class, put it in the drop box for our section, across from Math 410, on the 4th floor.

You're welcome to work on WebAssign problems together, using the "practice this problem" feature, but you must work out the solution to your problem (with the random numbers WebAssign chose for you) on your own. Similarly, you are welcome to work on the written homework together, but you must write up your final answers by yourself. Failure to abide by this policy constitutes cheating.

You are also generally welcome to use any resources you like to solve the problems. However, any resource you use other than the textbook (Stewart) must be cited in your written homework. This includes electronic resources (including Wikipedia and Google) and human resources (including the help room and your classmates). Failure to cite sources is plagiarism, a serious form of academic misconduct.

There is information on purchasing the textbook and WebAssign directly from the publisher at a reduced price on the Calculus Classes webpage.

### Students with disabilities

In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online. Registered students must present an accommodation letter to the professor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.

### Missed exams

If you have a conflict with any of the exam dates, you must contact me ahead of time so we can make arrangements. (At least a week ahead is preferable.) If you are unable to take the exam because of a medical problem, you must go to the health center and get a note from them -- and contact me as soon as you can.

## Syllabus and schedule.

Note: "+" indicates material not discussed in the textbook. Material in parentheses will probably be omitted from class (but discussed in problem sets). "-" indicates we only discuss parts of those sections not involving integrals.

Date Material Textbook Announcements
01/21 Brief overview. Distance, conic sections, polar coordinates. §10.3, 10.5, 10.6, 12.1 Welcome to V1201.
01/26 Coordinate systems in R3. Vectors in R2, R3, Rn. §12.1, 12.2,
pp. 1027-1028, 1033-1034

01/28 Dot product. Correlation. §12.3, +
02/02

Cross product.

§12.4

Written HW 1 due.
02/04 Equations for lines and planes (parametric, implicit). §12.5
02/09

More on lines and planes in space.

§12.5

Written HW 2 due.
02/11

Some more surfaces in space.

§12.6, +

02/16 Review.   Written HW 3 due.
02/18 Midterm 1.

02/23

Parametric curves.

§10.1, 10.2, 10.3, 13.1, 13.2

[CC, GS, Barnard drop deadline 02/24]
02/25

Derivatives and integrals of parametric curves. Arc length.

§13.2, 13.3

03/02

Curvature.

§13.3

Written HW 4 due.

03/04

Velocity, acceleration.

§13.4

03/09

Review of continuity and limits in one dimension.

§2.2, 2.4, 2.5

03/11

Continuity and limits of functions of several variables.

§14.1, 14.2

Written HW 5 due.
Spring break 03/16 - 03/20

03/23

More on limits and continuity.

§14.1, 14.2

03/25

Partial derivatives.

§14.3

Written HW 6 due.

03/30 Tangent planes and linear approximation. §14.4,
04/01

The chain rule.

§14.5 Written HW 7 due.
04/06

Review.

04/08 Midterm 2.
04/13 Directional derivatives. More linear approximation. Gradient. §14.6
04/15 Critical points and maximization. §14.7 Written HW 8 due.
04/20

More maximization: regions with boundary.

§14.7

04/22 Lagrange multipliers. §14.8 Written HW 9 due.
04/27 More Lagrange multipliers. §14.8
04/29 Review
05/04 Complex Numbers Appendix H Written HW 10 due.

## Written homework.

Written homework is always in addition to WebAssign homework.

## Handouts.

Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.

Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles. But if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours and the course TA in the help room. Talking to your other classmates can also be helpful. Finally, there is information about tutoring resources through CC / SEAS, GS, and Barnard here.

Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.