# MATH 2310 3.00AF (Fall 2010)Calculus of Several Variables with Applications Course Outline

### Description:

This course is designed to follow MATH 1300/1310, as the third semester in the standard university-level calculus sequence. It studies the calculus of functions in two and three dimensions, just as those earlier courses examined one-dimensional functions. For a function y=f(x), either x or y (or both) can be a vector. For example, if x is 1-dimensional but y is 2-dimensional, this means that f parametrizes a curve in the plane. While if x is 2-dimensional and y is 1-dimensional, the graph of f is a surface in space.

In addition to curves and surfaces, topics include vector functions, partial derivatives, gradients, polar coordinates, arc length, Lagrange multipliers, optimization, as well as multiple integrals and their changes of variables. If time permits, we will treat line integrals.

This is a required course for most honours and bachelor programs offered by the Department of Mathematics and Statistics. After this course, the study of calculus continues in MATH 3010.

### Prerequisites:

Integral calculus, normally MATH 1310 3.00; Students may also enter with MATH 1010 3.00 or MATH 1014 3.00; Students should have at least a high-school level knowledge of vectors in two and three dimensions.

Course Credit Exclusions are: MATH 2010 3.00 or MATH 2015 3.00

### Course Webpage:

www.math.yorku.ca/~salt/courses/2310f10/2310.html

### Instructor/Contact Information:

Tom Salisbury
Department of Mathematics and Statistics
• Departmental office: N520 Ross Building, (416) 736-5250, FAX: (416) 736-5757
• Undergraduate Program office: N502/503 Ross Building, (416) 736-5902
• Math/Stat lab: S525 Ross Building

### Lectures:

MWF 12:30-1:20pm in CB 121

### Office hours:

Wed. 2-3, Fri. 11-12

I will try to post a notice on the course webpage if other commitments make it necessary to reschedule one or more office hour. If you need to see me outside these hours, you are welcome to e-mail or call me to try to arrange an appointment.

### Math Lab

The Math department drop-in centre is located in S525 Ross. Variously called the Math Lab or the MathStat Lab, it is staffed with TAs who can help you with questions from the course. The hours are subject to change, but the plan is that it will start operation by at least the second week of classes, and will be open throughout the semester from Monday to Friday from 10:30 am to 3:30 pm. It will be closed during reading week. Hours during the exam period will vary.

### Text:

• Multivariable Calculus: Early Transcendentals by Stewart, 6th edition.
• Student solution manual to Stewarts's Multivariable Calculus
• Webassign
The text is basically the same as chapters 10-17 of the 6th edition of Stewart's Calculus: Early Transcendentals, so if you already own that, you may stick with it. We will be using the on-line homework facility WebAssign tied to the textbook. The York bookstore will sell a bundle that includes the text, solution manual, and WebAssign access. For those who already own Stewart from a previous course, it will be possible to purchase WebAssign access separately, at a lower price.

We will cover all of chapters 12-15. Background material from chapter 10 will be included when required. If time permits, we will cover the first 3 sections of chapter 16.

Note that the dates given for midterms and quizzes are tentative
• 20% First midterm exam (Wednesday October 27)
• 20% Second midterm exam (Friday November 26)
• 12% Quizzes (3 in total, held Wed. Oct. 6, Wed. Nov. 10, and Wed. Dec. 8)
• 13% Assignments (via WebAssign)
• 35% Final exam (3 hours, to be held during the exam period)

### Other information:

• Assignments are computer-graded. Quizzes will be graded by TAs. Exams will be graded by TAs and by the instructor, with the TAs doing more of the midterm grading, and the instructor more of the final grading.
• You are expected to do a minimum of 3-4 hours of homework per week. You don't learn how to do math by reading about it, or by watching someone else do it - you learn by struggling with problems yourself. The lectures will prepare you to do that, but the real learning in the course takes place while working problems (and more problems). The assigned homework is the minimum that will get you through the course. If you find it easy, you can get away with doing that minimum. But whenever you run up against something on the assigned homework, that you don't understand at first, you should follow it up by doing additional problems from the text, on the same topic.
• To get the most out of a lecture, you should read ahead and try some related problems beforehand. Don't fall behind, as each week builds on the previous one.
• All assignment, quizz, and exam marks should be interpreted as raw scores and not 'percentages'. Cutoffs will be announced for converting midterm scores into letter grades.
• There will be no makeup midterms or quizzes. If you miss one due to illness (with an acceptable note from your doctor), or some other valid reason then your final exam will simply be counted for more. This will be done by calculating an equivalent score for the missing work, based on your ranking on the final. If a makeup final examination is necessary, there will normally be a single sitting of that exam in January 2011.
• Students are responsible for reviewing the Student Information Sheet maintained by the university, which outlines policies on academic honesty, access and disability, religious observance accommodation, and student conduct.