Courant Institute New York University FAS CAS GSAS

# Contents

Author: Selin Kalaycioglu and NYU/CIMS Calc III Faculty January 24, 2011

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 1/24-28
10.1 Three-dimensional Coordinate Systems
10.2 Vectors
2 1/31-2/4
10.3 The Dot Product
10.4 The Cross Product
3 2/7-11
10.5 Equations of Lines and Planes
4 2/14-18
10.7 Vector functions and space curves
10.8 Arc length and Curvature
10.9 Motion in Space: Velocity and Acceleration
5 2/21-25
11.1 Functions of Several Variables
11.2 Limits and Continuity
6 2/28-3/4
11.3 Partial Derivatives
11.4 Tangent Planes and Linear Approximation
11.5 The Chain Rule
7 3/7-11
11.6 Directional Derivatives and the Gradient Vector
Review
Midterm (3/9)
8 3/14-18
No Classes SPRING BREAK
9 3/21-25
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
10 3/28-4/1
12.1
Double Integrals over Rectangles
12.2
Double Integrals over General Regions
12.3
Double Integrals in Polar Coordinates
11 4/4-8
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical Coordinates
12.7 Triple Integrals in Spherical Coordinates
12 4/11-15
13.1 Vector Fields
13.2 Line Integrals
13.3 The Fundamental Theorem of Line Integrals
13 4/18-22
13.4 Green's Theorem
13.5 Curl and Divergence
14 4/25-29
13.6 Parametric Surfaces and their Areas
13.7 Surface Integrals
15 5/2-6
13.8 Stokes's Theorem
13.9 The Divergence Theorem
16 5/9
Final Review

## Tuesday and Thursday Class Meetings

Week Dates Section Topics
1 1/24-28
10.1 Three-dimensional Coordinate Systems
10.2 Vectors
2 1/31-2/4
10.3 The Dot Product
10.4 The Cross Product
3 2/7-11
10.5 Equations of Lines and Planes
4 2/14-18
10.7 Vector functions and space curves
10.8 Arc length and Curvature
10.9 Motion in Space: Velocity and Acceleration
5 2/21-25
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
6 2/28-3/4
11.4 Tangent Planes and Linear Approximation
11.5 The Chain Rule
7 3/7-11
11.6 Directional Derivatives and the Gradient Vector
Review
Midterm (3/10)
8 3/14-18
No Classes SPRING BREAK
9 3/21-25
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
10 3/28-4/1
12.1
Double Integrals over Rectangles
12.2
Double Integrals over General Regions
12.3
Double Integrals in Polar Coordinates
11 4/4-8
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical Coordinates
12.7 Triple Integrals in Spherical Coordinates
12 4/11-15
13.1 Vector Fields
13.2 Line Integrals
13.3 The Fundamental Theorem of Line Integrals
13 4/18-22
13.4 Green's Theorem
13.5 Curl and Divergence
14 4/25-29
13.6 Parametric Surfaces and their Areas
13.7 Surface Integrals
15 5/2-6
13.8 Stokes's Theorem
13.9 The Divergence Theorem
Final Review

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