Prerequisites

Students who wish to enroll in Calculus III must meet the following prerequisites:

• Calculus II (V63.0122) with a C or higher.
• Our department's Calculus III placement test.
• A score of 5 on the Advanced Placement Calculus BC test does not per se qualify for enrollment in Calculus III.

See the math deparment's placement web page for more information.

Textbook and Materials

Essential Calculus, Early Transcendentals by James Stewart is the offcial text- book for the course.

Short Version: You need chapters 10-13 of Stewart's Essentail Calculus and access to Webassign. Webassign access may be purchased through the bookstore or directly through the course's Blackboard website.

Long Version: You need a textbook and you need WebAssign access. We have tried to provide as many options as possible for you to achieve this.

NYU has a custom imprint of this text which is sold bundled with access to Enhanced WebAssign. Enhanced WebAssign includes a hyperlinked electronic format of Stewart's Calculus, Early Transcen- dentals (of which Essentials is a slimmed-down version) accessible through the web.

In addition to the hardcover custom textbook, the NYU bookstore also has a limited number of looseleaf printings on three-hole punched paper, bundled with access to Enhanced WebAssign. These are less expensive up front, easier to carry around (since you don't have to carry the entire textbook at once), but cannot be sold back to the bookstore.

You may also buy the latest edition of Essential Calculus, Early Transcendentals, ISBN-13 978-0-495- 01428-7 non-customized, elsewhere. Then you can buy WebAssign (regular or Enhanced with Stewart's Calculus, Early Transcendentals) from them online directly.

Finally, you may decide to go completely electronic. You may buy online (through iChapters) an electronic format of Essential Calculus, Early Transcendentals, or a subset of that text consisting of which chapters you will need. This will be the exact same text, problem numbering, section number- ing, and pagination as the official edition, but is not hyperlinked. With this you could buy regular WebAssign without the electronic text included. Or, you may buy Enhanced WebAssign alone, and we will provide the correspondence between problems assigned in Essentials with those from the full version of Calculus. Or, of course, you could buy both the electronic format of Essential Calculus, Early Transcendentals, and Enhanced WebAssign which includes the hyperlinked version of Essential Calculus, Early Transcendentals.

Which one is right for you? If you want to minimize your total costs but want some kind of paper textbook, it's either a used textbook and regular WebAssign or the official looseleaf edition which includes Enhanced WebAssign. If you don't desire a paper text, get Enhanced WebAssign and nothing else.

If you want the most textbook for your dollar, you probably want one of the paper textbook plus EnhancedWebAssign bundles sold in the bookstore. You'll have the full paper version with no confusion about staying in sync with the instructor, and the full hyperlinked electronic version. The hardcover can be sold back, but the looseleaf is more convenient.

A graphing calculator is encouraged for class discussion and on homework, but not allowed for exams. No specific calculator is endorsed, so do not buy a new one. If you have one already, continue to use that one; if you do not, try free alternatives such as Wolfram Alpha.

Homework

There are two media for homework in Calculus III.

There will be weekly online assignments administered through WebAssign (This is why a WebAssign software license is one of the required course materials), WebAssign problems are computational in nature and assess the techniques introduced in class. Many of these problems will resemble examples in the textbook or from class. You will get immediate feedback on your progress and will get several chances to ensure it.

There will also be problems to write up on paper each week and turn in. These problems will require more than just procedure, might connect two more more things together, and will more closely resemble the harder exam problems.

One of the major goals of college-level mathematics education is to move students from computational processes to conceptual thinking and communication. That is the biggest difference between this course and a high school course, even an Advanced Placement course. Mathematics is more than a bag of tricks and there are not a limited number of \types" of problems that can be asked. The goal in class is to prepare you to do the homework and not necessarily to show you how to do your homework. The

learning occurs when you can move yourself into the unknown territory. Graders will grade the written homework promptly, and solutions will be made available on the course website. Graders will be expecting you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for unexplained answers.

In fairness to fellow students and to graders, late homework will generally not be accepted. Because sometimes things more important than math homework come up, you have some free passes: Your lowest two written assignment score and your three lowest WebAssign scores will be dropped in the final grade calculation.

By all means you may work in groups on the homework assignments. Collaboration is a big part of learning and of scholarship in general. However, each student must turn in his or her own write-up of the solutions, with an acknowledgment of collaborators.

Exams

There will be one midterm exam, held in class on Thursday, March, 10th.

The final exams for all lectures are scheduled on Thursday, May 12th from 2:00-3:50 pm. Please make a note of your final exam time and plan your travel schedule accordingly.

Exams will contain a mixture of computational and conceptual problems. Some of them will resemble homework problems, while some will be brand new to you.

Grading policy

Grades will be computed by a weighted average:

Midterm 20%
WebAssign 10%
Written Homework 15%
In-Classwork 15%
Final 40%
Total 100%

We will convert this score to a letter grade beginning with these values as cutos:

93 A
90 A-
87 B+
83 B
80 B-
75 C+
65 C
50 D

As for a curve, these cutoffs might be adjusted, but only in the downward direction (to make letter grades higher).

Week	Topic
1	Three dimensional coordinate systems Vectors
2	The Dot Product The Cross Product
3	Equations of Lines and Planes Cylinders and Quidric Surfaces
4	Vector functions and space curves Arc length and Curvature Motion in Space: Velocity and Acceleration
5	Functions of Several Variables Limits and Continuity Partial Derivatives
6	Tangent Planes and Linear Approximation The Chain Rule
7	Directional Derivatives and the Gradient Vector MIDTERM
8	Spring Break-No Classes
9	Maximum and Minimum Values Lagrange Multipliers
10	Double Integrals over Rectangles Double Integrals over General Regions Double Integrals in Polar Coordinates
11	Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates
12	Vector Fields Line Integrals The Fundamental Theorem of Line Integrals
13	Green's Theorem Curl and Divergence
14	Parametric Surfaces and their Areas Surface Integrals
15	Stokes' Theorem The Divergence Theorem
16	Review for Final