Week of

Section

Topic

  1/07 – 1/11

1.1

Chapter 0: 

Chapter 1.1: Cartesian Coordinates:  In 2 and 3 dimensional space

1.2

Vectors in 2 and 3 Dimensions:

1.2

Continue study of vectors

1.3

The Angle Between Two Vectors:  The Dot Product

1/14 – 1/18

1.4     

The Cross Product:

1.5

Lines and Planes in 3-dimensional Space

More on equations of lines and planes

2.1

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

1/21

Monday

Holiday

  1/22 – 1/25

2.2

Parameterized Curves in Space:  Newton’s second law.  Begin free fall under gravity.  Projectile motion under gravity; The isotropic oscillator (Optional)

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

1/29

2.4

More on the geometry of curves in space; the osculating circle, and the normal and tangential components of acceleration

Review for Test #1

January 30

Wednesday

TEST #1

1/31

3.1

Multivariable Functions:  Material up through level curves

  2/4 – 2/8

3.1

Multivariable Functions:  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;

  2/11 – 2/15

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.

What does the gradient vector say about a function?

  2/18 – 2/22

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;

2/26

4.1

Double Integrals over a rectangle

as a limit of Riemann sums

Review for Test #2

February 27

Wednesday

TEST #2  

  2/28

4.1

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

4.1

Double integrals over general regions

3/4 – 3/8

4.1

Reversing the order of integration

4.2

Applications of Double Integrals

4.3

Triple Integrals in Cartesian Coordinates: Over rectangular solid regions

   3/11 – 3/15

Spring Break

3/18 – 3/22

4.3

Triple integrals over z-simple regions

Triple integrals over x & y- simple regions; Applications of triple integrals

5.1

Double Integrals in Polar Coordinates: over polar rectangles

5.1

Double integrals in polar coordinates over more general regions

3/25 – 3/29

5.2

Triple integrals in cylindrical coordinates

5.3

Triple integrals in spherical coordinates                                                        

5.3

More on triple integrals in spherical coordinates

6.1

Vector Fields                                    

4/2

6.2

Line Integrals of functions:

Review for test #3

4/3

Wednesday

TEST #3

4/4

6.3

Line integrals of vector fields:  The fundamental theorem for line integrals Conservative vector fields and potential functions; Conservation of total energy

4/8 – 4/12

6.4

 Parametric Surfaces in Space: graphs, spheres and cylinders

 6.4

Surface Integrals: Surface Area of a Parametric Surface

Tangent planes to parametric surfaces

6.5

Surface Integral of a Function

6.5

Surface Integral of a Vector Field

4/16

 6.5

More on surface integrals of vector fields                    

Review for test #4

4/17

Wednesday

TEST #4

4/18

7.1

7.2

Integral Curves of Vector Fields

The Divergence of a Vector Field

4/19

Friday

Holiday

4/22 – 4/26

7.2

The Curl of a Vector Field:

7.3

Green’s Theorems:  for circulation and for flux

7.4, 7.5

Stokes’ Theorem, The Divergence Theorem

Last day of classes

Semester Summary

5/7

Tuesday

FINAL EXAM:    1 – 4pm