Courant Institute New York University FAS CAS GSAS

# Contents

Author: Alex Hanhart and NYU/CIMS Calc III Faculty September 07, 2010

This is a week-by-week calendar of topics covered in Calculus III. As a rule of thumb, the topics are generally to be spread out equally during the week, so if there are two topics, each one takes one class period, while if there are three, each should take two-thirds of a class period.

Please note that these schedules are tentative and subject to change by your indiuvidual instructor. Regardless it still provides a complete list of topics for the semester and a rough idea of when the topics will be covered.

# Course topics by week

## Monday and Wednesday Class Meetings

Week Dates Section Topics
1 9/6-9
10.1 Three-dimensional Coordinate Systems
2 9/13-16
10.2 Vectors
10.3 The Dot Product
3 9/20-23
10.4 The Cross Product
10.5 Equations of Lines and Planes
4 9/27-30
10.7 Vector functions and space curves
10.8 Arc length and Curvature
5 10/4-7
10.8
Arc length and Curvature
10.9 Motion in Space: Velocity and Acceleration
11.1 Functions of Several Variables
11.2 Limits and Continuity
6 10/11-14
11.2 Limits and Continuity
11.3 Partial Derivatives
7 10/18-21
11.4 Tangent Planes and Linear Approximation
Review
Midterm (10/20)
8 10/25-28
11.5 The Chain Rule
11.6 Directional Derivatives and the Gradient Vector
9 11/1-4
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
10 11/8-11
12.1 Double Integrals over Rectangles
12.2 Double Integrals over General Regions
12.3 Double Integrals in Polar Coordinates
11 11/15-18
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical Coordinates
12.7 Triple Integrals in Spherical Coordinates
12 11/22-25
13.1 Vector Fields
13.2 Line Integrals
13 11/29-12/2
13.3 The Fundamental Theorem of Line Integrals
13.4 Green's Theorem
13.5 Curl and Divergence
14 12/6-9
13.6 Parametric Surfaces and their Areas
13.7 Surface Integrals
13.8 Stokes's Theorem
15 12/13-16
13.9 The Divergence Theorem
Review

## Tuesday and Thursday Class Meetings

Week Dates Section Topics
1 9/6-9
10.1 Three-dimensional Coordinate Systems
10.2 Vectors
2 9/13-16
10.3 The Dot Product
10.4 The Cross Product
3 9/20-23
10.5 Equations of Lines and Planes
4 9/27-30
10.7 Vector functions and space curves
10.8 Arc length and Curvature
10.9 Motion in Space: Velocity and Acceleration
5 10/4-7
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
6 10/11-14
11.4 Tangent Planes and Linear Approximation
11.5 The Chain Rule
7 10/18-21
11.6 Directional Derivatives and the Gradient Vector
Review
Midterm (10/21)
8 10/25-28
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
9 11/1-4
12.1
Double Integrals over Rectangles
12.2
Double Integrals over General Regions
12.3
Double Integrals in Polar Coordinates
10 11/8-11
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical Coordinates
12.7 Triple Integrals in Spherical Coordinates
11 11/15-18
13.1 Vector Fields
13.2 Line Integrals
13.3 The Fundamental Theorem of Line Integrals
12 11/22-25
13.4 Green's Theorem
13 11/29-12/2
13.5 Curl and Divergence
13.6 Parametric Surfaces and their Areas
13.7 Surface Integrals
14 12/6-9
13.8 Stokes's Theorem
13.9 The divergence Theorem
15 12/13-16
Review

For final exam days and times by class meeting time, please see the registrar's exam page.