Modified
schedule due to covid-19 pandemic
MA
242.601 - Spring 2020
Day-by-day Schedule
|
Week of |
Section |
Topic |
|
1/06– 1/10 |
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 |
|
|
|
|
|
1/13
– 1/17 |
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 |
|
|
|
|
|
1/20 |
Monday |
Holiday |
|
1/21 – 1/24 |
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 |
|
|
|
|
|
|
1/27
– 1/31 |
2.4 |
More on the geometry of curves in space;
the osculating circle, and the normal and tangential components of
acceleration |
|
|
3.1 |
Multivariable Functions:
Material up through level curves |
|
|
|
Review
for Test #1 |
|
January 31 |
Friday |
TEST #1 (********** 2-day window: 1/30 or 2/3
*************) |
|
|
|
|
|
2/3 – 2/7 |
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; |
|
|
|
|
|
|
2/10 – 2/14 |
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? |
||
|
|
|
|
|
2/17 – 2/21 |
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; |
|
|
|
Review
for Test #2 |
|
|
|
|
|
|
Monday, 2/24 |
Monday |
TEST #2 (********** 3-day
window: 2/21, 2/24, 2/25 *************) |
|
2/25 - 2/28 |
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 |
|
|
|
|
|
3/2
– 3/6 |
4.1 |
Reversing
the order of integration |
|
4.2 |
Applications of Double Integrals |
|
|
4.3 |
Triple Integrals in Cartesian Coordinates: Over
rectangular solid regions |
|
|
|
|
|
|
3/09 – 3/13 |
|
Spring Break |
|
|
|
|
|
3/16 – 3/20 |
|
Extra week of spring break due to
Covid-19 pandemic |
|
|
|
|
|
|
|
|
|
3/23 – 3/27 |
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 |
|
|
|
5.2 |
Triple integrals in cylindrical coordinates |
|
|
|
|
|
3/30 |
Monday |
TEST #3 – Take home test
with open book and open notes |
|
3/31
– 4/03 |
5.3 |
Triple integrals in spherical coordinates |
|
5.3 |
More
on triple integrals in spherical coordinates |
|
|
6.1 |
Vector Fields |
|
|
6.2 |
Line Integrals of functions: First briefly review parameterized
curves from section 2.2 and formula #2.6 for ds/dt in section 2.3. |
|
|
|
|
|
|
4/06
– 4/10 |
6.3 |
Line integrals of vector fields:
The
fundamental theorem for line integrals |
|
6.3 |
Conservative
vector fields and potential functions; Conservation of total energy |
|
|
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 |
|
|
|
|
|
|
4/13
– 4/17 |
6.5 |
Surface Integral of a
Vector Field |
|
|
More on surface integrals of vector fields |
|
|
Wednesday |
TEST #4 – Take home test
with open book and open notes |
|
|
7.2 |
The Divergence of a Vector Field |
|
|
7.2 |
The Curl of a Vector Field: |
|
|
|
|
|
|
4/20 |
|
Green’s Theorems: for circulation
and for flux |
|
4/21 |
|
Stokes’ Theorem |
|
4/22 |
|
The Divergence Theorem. |
|
4/23 |
|
Review
day; LAST DAY OF
CLASSES |
|
|
|
|
|
4/24 |
Friday |
Reading Day |
|
|
|
|
|
4/27
|
Monday |
|
|
4/28 |
Tuesday |
|
|
4/29 |
Wednesday |
Day 1 of 2-day window for FINAL EXAM –
take home exam open book open notes |
|
4/30 |
Thursday |
Day 2 of 2-day window for FINAL EXAM–
take home exam open book open notes |