Week of

Section

Topic

  8/22 – 8/24

1.1

Cartesian Coordinates:  In 2 and 3 dimensional space

1.2

Vectors in 2 and 3 Dimensions:

1.2

Continue study of vectors

  8/27 – 8/31

1.3

The Angle Between Two Vectors:  The Dot Product

1.4

The Cross Product:

1.5

Lines and Planes in 3-dimensional Space

More on equations of lines and planes

9/3

Monday

Holiday

9/4 – 9/7

2.1

The Calculus of Vector-valued Functions:  Limits, derivatives and integrals

2.2

Parameterized Curves in Space:   Newton’s second law.  Free fall under gravity.  

2.2

Projectile motion under gravity.

  9/10 – 9/14

2.3

Fundamental Quantities Associated with a Curve: Tangent vectors, arc length and curvature

2.4

The Intrinsic Geometry of Curves in 3-Space; curvature and the osculating plane

2.4

More on the geometry of curves in space; the osculating circle

2.5

The decomposition of the acceleration vector into its normal and tangential components and the formula

Review for Test #1

September 17

Monday

TEST #1

  9/18 – 9/21

3.1

Multivariable Functions:  Material up through level curves

Level surfaces of functions of 3 variables.  Parametric surfaces.

3.2

Limits and Continuity:  Theorems on limits; Continuity;

3.3

Directional Derivatives: Partial derivatives;  higher derivatives;

  9/24 – 9/28

3.3

Geometrical interpretation of partial derivatives; Tangent plane to the graph of f(x,y)

3.4

Differentiability of multivariable functions:  Definition; Differentiability and continuity; Theorem 9 on characterizing differentiability.

3.5

The Directional Derivative and the Gradient:  Formula for the directional derivative in terms of the gradient (Corollary 2).

What does the gradient vector say about a function?

  10/01 – 10/03

3.5

The Chain rules for multivariable functions

Tangent planes to graphs z = f(x,y);  The general chain rule

3.6

Optimization: local and global extreme values of f(x,y)

3.6

More on extreme values

10/4 – 10/5

Thursday-Friday

Fall Break

  10/8 - 10/10

4.1

Double Integrals over a rectangle as a limit of Riemann sums

Fubini’s Theorem for double integrals over rectangles; iterated integrals

4.1

Double integrals over general regions

10/11

Thursday

Review for Test #2

10/12

Friday

TEST #2

4.1

Reversing the order of integration;

4.2

Applications of Double Integrals

More on applications of double integrals

10/22 – 10/26

4.3

Triple Integrals in Cartesian Coordinates: Over rectangular solid regions

Triple integrals over  z-simple regions

Triple integrals over x- and y- simple regions

Applications of triple integrals

10/29 – 11/02

5.1

Double Integrals in Polar Coordinates: over polar rectangles

Double integrals in polar coordinates over more general regions

5.2

Triple integrals in cylindrical coordinates

Friday

Review for test #3

11/05

Monday

TEST #3

11/06 – 11/09

5.3

Triple integrals in spherical coordinates

5.3

More on triple integrals in spherical coordinates

6.1

Vector Fields

6.2

Line Integrals: First briefly review parameterized curves from section 2.2 and formula #2.6 for ds/dt in section 2.3. 

 11/12 – 11/16

6.2

­ Line integrals of functions

6.3

Line integrals of vector fields:  The fundamental theorem for line integrals

5.3

Conservative vector fields and potential functions; Conservation of total energy

6.4

Parametric Surfaces in Space: graphs, spheres and cylinders

11/19 – 11/20

6.5

Surface Integrals: Surface Area of a Parametrized Surface

Tangent planes to parametric surfaces

6.5

Surface Integral of a Function

11/21 – 11/23

Thanksgiving Holiday

11/26

6.5

Surface Integral of a Vector Field 

11/27

Tuesday

Review for test #4

11/28

Wednesday

TEST #4

11/29

7.1

7.2

Integral Curves of Vector Fields

The Divergence of a Vector Field

11/30

7.2

The Curl of a Vector Field:

Maxwell’s Equations and Electromagnetic Waves (Optional)

12/3 – 12/7

Last week

Of

Classes

7.3

Green’s Theorems:  for circulation and for flux

7.4

Stokes’ Theorem

7.5

The Divergence Theorem

Thursday

Semester Review

Friday

Semester Review