CalcIIISyllabusFa12x - John Pais

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Calculus III: 2012

13

Ladue Horton Watkins High School



Instructor:

Dr. John Pais

Overview:

This course is an introduction to the study of curves and surfaces in three dimensional Euclidean
space. For the first time in their mathematical development
students will acquire the tools
necessary to represent and analyze both the motion of particles and the forces acting on them in
the proper geometrical setting. In addition, this course will not only develop high level
mathematics skills, but also emphasiz
e problem solving techniques, examine the necessity of
mathematics as it relates to career goals, enable students to communicate mathematically, and
illustrate the connec
tion to real
-
world application.

Learning takes place through many types of activities
we engage in during each ninety
-
minute
period we meet. While mastery of formal objectives may be measured through tests, quizzes,
and projects, other important skills developed in class are not so easily measured in traditional
assessments. Students who
attend with the intent to learn will construct knowledge both
formally and informally. When the entire group comes to the classroom prepared to learn, an
environment conducive to growth is created.

Course Description:

Calculus III

is a continuation of the

material covered in AP Calculus BC. Topics covered include
vectors and curves in two and three dimensions, quadric surfaces, partial derivatives, extrema
(maxima and minima), Lagrange multipliers, vector fields in two and three dimensions, double
and trip
le integrals, Green’s Theorem, Stokes Theorem, Divergence Theorem, and differential
equations. Graphing calculators and
MAPLE®

software are used throughout the course. It is
recommended that students have a grade of B or better in AP Calculus BC before enr
olling in the

course.

Methods of Instruction:

Class time is spent primarily in an interactive lecture/discussion/practice problem
-
solving format
which includes question and answer sessions, class discussion, interactive visual
-
ization, guided
practice,
note taking, and seat work.

Classroom Expectations:

1. Be in your assigned seat, prepared and ready to work, when the bell rings.

2. Talk when it is appropriate
-

do not interrupt someone else who is speaking.

3. Follow directions the first time they ar
e given.

4. Always respect other people, property, and yourself.

5. Cell phones should be turned off during the school day. Students should not listen to music
during class.

Grades:

Grades are determined on total points earned. Points are earned throug
h tests, quizzes, warm
-
ups, homework checks, homework quizzes, projects, and in
-
class activities. This is a yearlong
course and so a final exam is given at the end of each semester worth twenty percent of the
semester grade.


Grading Scale:


H 97
-

1
00% B 83
-

86% C
-

70
-

72% F Below 60%


A 93
-

96% B
-

80
-

82% D+ 67
-

69%


A
-

90
-

92% C+ 77
-

79% D 63
-

66%


B+ 87
-

89% C 73
-

76%


D
-

60
-

62%

Homework:

In order to receive credi
t for a homework check, the assignment should be complete, the
problems written out, and all the necessary work shown. If the student does not know how to do
a problem, something should still be written for the problem to show that the problem was
attempt
ed. All work should be done neatly and kept in each student’s math notebook.
Incomplete homework will receive half credit or less.

Homework will also be checked through homework quizzes. Unannounced homework quizzes
will be given frequently, so it is
very important to keep up with daily homework.

Materials for Class and Website:

Each class day students should bring their math notebook or folder, pencils or pens, paper,
assignments, and a calculator. Course materials and activities will be posted on (li
nked to) the
class website located at
http://drpcourses.blogspot.com/
.

It is a
requirement of the course that the website

be checked often
, since all course
in
formation will be posted there.



Attendance/Ta
rdies:

The school policy will be followed regarding absences and tardies (see your student planner).
Please remember that, according to district policy, absences not cleared within twenty four hours
of the absence are unexcused. Unexcused absences will
result in a zero for the assignments and
activities for that day.

Makeup Work Due to Absence:

A one week deadline is given to makeup all missed assignments and tests. Tests may be made
up during Academic Lab. If assignments, quizzes, and tests are not com
pleted within one week
of an absence, students will receive a zero. If the absence has been an extended absence due to
special circumstances, please see me and we’ll make appropriate arrangements. Please
remember that, according to district policy, you w
ill not be allowed credit for any work due or
assigned on t
he day of an unexcused absence.

Communication:

I look forward to an exciting and successful school year! At any time if you have any questions
or concerns, please ask me. I am usually available in

the math office for help before or after
school and during Academic Lab. In addition, the best way to reach me at school is via e
-
mail
jpais@ladueschools.net

.


Resources

(T
extbook

-

Stewart
):

Auroux, Denis.
Multivariable Calculus.
Mathematics 18.02
, MITOPENCOURSEWARE,
Massachusetts Institute of Technology, Fall 2007. Web. 23 July 2010.


Fleisch, Daniel.
A Student's
Guide to Maxwell's Equation.

New York, NY: Cambridge
University Press, 2008.


Marsden, Jerrold E., Tromba, Anthony J.
Vector Calculus, 5th Edition.

New York, NY: W. H.
Freeman and Company, 2003.


Murray, Daniel A.
Differential and Integral Calculus.

New York, NY: Longmans, Green, and
Company, 1908.


O'Neill, Barrett.
Elementary Differential Geometry, Revised 2nd Edition.
Burlington, MA:
Academic Press Elsevier, Inc., 2006.


Stewart, James.
Multivariable Calculus, 6E
. Belmont, CA: Brooks/Cole, 2008.




Detailed Syllabus with Active Links to Resources



Unit 1
.1
: Vectors and 3D Space Geometry
-

3D Coordinates

Local Objective



Plot

points in 3
D coordinate systems.



Perform algebraic oper
ations and transformations in 3
D coordinate systems.



Use
graphing software to visualize 3D points and transformations of these points.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click here:

Interactive Quiz 13.1

This assessment may be
used either as an homework quiz or as a small group quiz.




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 1
-
5 apply to this objective.

Learning Activity

PowerP
oint
slides address
ing

the current objective
.

Click here:

Chapter 13 Section 1


Homewor
k

Stewart Chapter 13.1: 7
-
15 (odd), 19, 21, 31




Unit 1
.2
: Vectors and 3D Space Geometry
-

3D Vectors

Local
Objective



Plot and compute with

3D vectors.



Use the standard basis to represent vectors.




Create a vector from two points.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 13.2




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 6
-
10 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter

13 Section 2


Homework

Stewart Chapter 13.2
:
13
-
23 (odd), 31, 35, 4
1



Unit 1
.3
: Vectors and 3D Space Geometry
-

Dot Product

Local
Objective



Compute the dot product of two 3D vectors and use the related theorems.



Relate the magnitude of a vector to the dot product of the vector
with
itself.



Use the magnitude of a non
-
zero vector to create a unit vector with the same
direction.



Find the angle between two vectors.

Formative Assessment

-

Online interactive quizzes an
d tu
torials correlated to textbook
(Stewart)

c
hapters and sections.


Click here:

Interactive Quiz 13.3




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 11
-
13 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 13 Section 3


Homework

Stewart Chapter 13.3: 23
-
29 (odd), 37, 41, 45, 49, 51, 53



Unit 1
.4
: Vectors and 3D Space Geometry

-

Cross Produc
t

Local
Objective



Compute the cross product of two 3D vectors and use the related theorems.



Use the algebraic properties of the dot product in combination with the cross
product.



Relate the magnitude of the cross product to the area of the
parallelogram made by
the two vectors.



Use the cross product to find the angle between two vectors.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click here:

Interactive Quiz 13.4




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 14
-
17 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 13 Section 4

Homework

Stewart Chapter 13.4: 5, 7
,
11,
19, 2
9
, 3
3, 37, 43, 49




Unit 1
.5
: Vectors and 3D Space Geometry
-

Lines and Planes

Local
Objective



Use
the vector definitions of lines and planes.



Formulate and solve geometric problems involving lines and planes using vectors.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click
here:

Interactive Quiz 13.5




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 14
-
17 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 13 Section 5

Homework

Stewart Chapter 13.5: 5, 7, 11, 17, 23, 29, 43, 53, 55



Unit 1
.6
: Vectors and 3D Space Geometry
-

Cylinders and Quadric Surfaces

Local
Objective



Formulate and solve geometric problems involving lines, planes, cylinders, and
quadric surfaces.



Plot lines, planes, cylinders, quadric surfaces, and figures constructed from these.


Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 13.6



Summative Assessment

-

Studen
ts are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 11
-
15 and 17 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 13 Section 6


Homework

Stewart Chapter 13.6: 3
-
17 (odd), 33, 41
,
43


Unit 1 Test



Unit 2
.1
: Space Curves

-

2D and

3D
Space Curves

Local
Objective



Write parametric and vector equations of space curves.



Use technology to graph

space curves.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click here:

Interactive Quiz 14.1




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 14 Test

Questions 1
-
3 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter

14 Section 1




Homework

Stewart Chapter 14.1: 1
-
19 (odd), 27, 41


Unit 2
.2
: Space Curves

-

Derivatives and Integrals

Local
Objective



Compute componentwise

limits, derivatives, and integrals of space curves.



Use technology to graph space curves.



Use
space curves to model particle motion.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 14.2




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 14 Test

Questions 4
-
5, 8
-
9 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 14 Section 2


Homework

Stewart Chapter 14.2: 5
-
37 (odd)





Unit 2
.3
: Space Curves
-

2D Arc Length and Curvature

Local
Objective



Compute the arc length of curves in the plane.



Compute the classical curvature and radius of curvature of curves in the plane.

Learning Activity

Material from the supplementary textbook (Murray) provides students with perspective on how
mathematicians thought about curvature over 100 years ago!
Interestingly, this point of view is a
natural continuation of the material learned in their previous calculus course.


This classical
perspective is in contrast to the modern differential geometric perspective they will learn in
Calculus III.

Click here:

(Murray) Articles 95
-
105


Homework

Murray: Art. 95, p. 6, 1
-
3;
Art. 96
,

p. 10, 1
-
2
;

Art. 99
,

p. 13, 1
;

Art. 100, p. 14, 1
-
2;

Art. 101, p.
18, 3;
Art. 103,
p. 23, 3
;

Art. 104, p. 29, 2;
Art. 105, p. 31, 1.




Unit 2
.4
: Space Curves
-

3D Arc Length and Curvature

Local
Objective



Compute the arc length of 3D space curves.



Compute the classical curvature and radius of curvature of 3D space curves.

Formative
Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 14.3




Summative
Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 14 Test

Questions 10
-
12 apply to this objective.

Learning Activity

PowerP
oint slides addres
s
ing

the current objective.

Click here:

Chapter 14 Section 3



Homework

Stewart Chapter 14.3: 1
-
11 (odd)




Unit 2
.5
: Space Curves
-

2D and 3D Motion

Local
Objective



Use space curves to model 2D and 3D

motion.




Interpret the appropriate derivatives as velocity and acceleration.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 14.4




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 14 Test

Questions 13
-
20 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 14 Section 4


Homework

Stewart Chapter 14.4: 3
-
15 (odd)
, 33
-
37 (odd), 41



Unit 2
.6
: Spac
e Curves
-

Arc Length Reparamete
rization

Local
Objective



Use various
function to reparameterize a space curve.



Use unit speed reparameterizations to simplify analysis of 3D space curves.

Formative Assessment

-

This quiz is correlated to the corresponding material drawn from a
supplementary textbook (O'Neill).
Click here:

Arc Length Reparametrization Quiz



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Frenet Frames Test

Questions 1
-
4 apply to this objective.

Learning Activity

Material for this unit is drawn from a supplementary textbook (O'Neill).

Click here:


(O'Neill) Chapter 2 Section 2


Homework

Stewart Chapter 14.3: 13
-
14
, more TBD




Unit 2
.7
: Space Curves
-

Frenet Frame Fields

Local
Objective



Create moving
Frenet Apparatus to represent intrinsic geometry of a space curve.



Use unit speed reparameterization to simplify computation of

Frenet Apparatus.

Formative Assessment

-

This quiz is correlated to the corresponding material drawn from a
supplementary textb
ook (O'Neill).
Click here:

Introduction to Frenet Frames Quiz



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Frenet Frames Test

Questions 5
-
8 apply to this objective.

Learning Activity

Material for this unit is drawn from a supplementary textbook (O'Neill).

Click here:


(O'Neill) Chapter 2 Section 3A


Homework

Stewart Chapter 14.3: 17
-
20, more TBD




Unit 2
.8
: Space Curves
-

Curvature, Torsion, and the Frenet Apparatus

Local
Objective



Find the rate of change of the Frenet Apparatus

using the curvature and torsion
of

the space curve.



Relate the intrinsic geometry of a space curve to its curvature and torsion.

Formative Assessment

-

This quiz is correlated to the corresponding
material drawn from a
supplementary textbook (O'Neill).

Click here:

Curvature, Torsion, and Frenet Apparatus Quiz



Summative Assessment

-

Students are assessed over the en
tire unit.

Click here:

Frenet Frames Test

Questions 9
-
13 apply to this objective.

Learning Activity

Material for this unit is drawn from a supplementary textbook (O'Neill).

Click here:


(O'Neill) Chapter 2 Section 3B


Homework

Exercises 3.1
-
3.3 in the O’Neill
notes above.

Also, think about how to prove Theorem 3.3.


Unit 2

Test



Unit 3
.1
: Partial Derivatives
-

Functions of Several Variables

Local
Objective



Construct and compute

with functions from
n
-
dim real space to
m
-
dim real space.



Interpret geometrical representation of functions from
n
-
dim real space to
m
-
dim
real space.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.1



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 1 and 3 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.


Click here:

Chapter 15 Section 1


Homework

Stewart Chapter 15.1: 1, 7
-
19 (odd), 39
-
47 (odd), 61
-
65 (odd)



Unit 3
.2
: Partial Derivatives
-

Limits and

Continuity

Local
Objective



Define and

compute limits

for functions from
n
-
dim real space to
m
-
dim real space.



Define and test for continuity of functions from
n
-
dim real space to
m
-
dim real
space.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.2



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15

Test

Questions 1, 2, and 10 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 2



Homework

Stewart Chapter 15.2: 5
-
18 (odd), 29
-
37 (odd)




Unit 3
.3
: Partial Derivatives
-

Definition and Computation

Local
Objective



Define and

compute

partial derivatives

for functions from
n
-
dim real space to
m
-
dim real space.




Define and use partial derivative rules to compute partial derivatives.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.3



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions

4, 5, 8, and 14 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 3



Homework

Stewart
Chapter 15.3: 1, 15
-
66 (multiples of 3)




Unit 3
.4
: Partial Derivatives
-

Tangent Planes

Local
Objective



Use partial derivatives of a function from






to define the tangent

plane of an
implicit surface in



.



Use differential notation to compute tangent plane approximation of an implicit
surface at a given point.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.4



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 6, 7, and 15 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 4


Homework

Stewart Chapter 15.4: 1
-
17

(odd)



Unit 3
.5
: Partial Derivatives
-

The Chain Rule

Local
Objective



Use va
rious forms of the chain rule for

a function fro
m








.



Use the chain rule to

compute (partial)

implicit derivatives.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.5



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 9 and 14 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 5



Homework

Stewart Chapter 15.5: 1
-
14

(
all
)
, 17
-
25 (odd)



Unit 3
.6
: Partial Derivatives
-

Directional Derivatives

Local
Objective



Define and

compute the directional derivative of functions from






and





.



Use
the directional derivative to find the direction and maximum r
ate of change
of

functions
from






and





.



Use the gradient operator to define and compute the directional derivative.

Formative Assessment

-

Online interactive quizzes and t
u
torials correlated to textbook
(Stewart)

c
hapters and sections.


Click here:

Interactive Quiz 15.6



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 11
-
13 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 6



Homework

Stewart Chapter 15.6: 5
-
25 (odd), 33, 37, 39
-
43 (odd)



Unit 3
.7
: Partial Derivatives
-

Maxima and

Minima

Local
Objective



Use partial derivatives to find local extrema (maxima, minima)

in a given direction.



Use partial derivatives to find critical points of an implicitly defined surface.



Use the second partial derivative test

(Hessian determinant) to analyze the geometry
of an implicitly defined surface in terms of local extrema and saddle points.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stew
art)

chapters and sections.


Click here:

Interactive Quiz 15.7



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 16
-
19 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 7


Homework


Stewart Chapter 15.7: 5
-
19 (odd), 29
-
35 (odd)




Unit 3
.8
: Partial Derivatives
-

Lagrange Multipliers

Local
Objective



Use Lagrange multipliers to find maxima and minima of a function with respect to a
given constraint.



Apply Lagrange multipliers to solve a variety of interesting problems taken

from
geometry, engineering, science, and economics.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 15.8



Summative Assessment

-

Studen
ts are assessed over the entire unit.

Click here:

Chapter 15 Test

Questions 19 and 20 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 15 Section 8



Homework

Stewart Chapter 15.8: 3
-
21 (odd)


Unit 3

Test



Unit 4
.1
: Vector Fields
-

2D Mappings and Plots

Local
Objective



Define a 2D

vector field F from








and plot it as a vector attached to each
point.



Given the plot of a 2D vector field, find or match an appropriate function that
represents the geometry of the field.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.



Click here:

Interactive Quiz 17.1

This assessment may be used either as an homework quiz or
as a small group quiz.




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Vector Fiel
ds Visual Representation Quiz

Questions 1
-
6 and 11
-
14 apply to this
objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter
17 Section 1



Homework

Stewart Chapter 17.1: 1
-
6 (all), 11
-
14 (all)



Unit 4
.2
: Vector Fields
-

3D Mappings and Plots

Local
Objective



Define a 3D

vector field
F from







and plot it as a vector attached to each
point.



Given the plot of a 3D vector field, find or match an appropriate function that
represents the geometry of the field.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.1

(Intentionally used for both
2D and 3D formative assessment.)


Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Vector Fields Visual Representation Quiz

Questions 7
-
10 and 15
-
18 apply to this
objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 1



Homework

Stewart Chapter 17.1: 7
-
10 (all), 15
-
18 (all)




Unit 4
.3
: Vector Fields
-

2D Gradient, Divergence, and Curl

Local
Objective



Define a 2D
vector field as the gradi
ent of a scalar function f from






.



Recognize when a 2D vector field F is or is not the gradient of a scalar function f.



Use the gradient operator to define the divergence of a vector field.



Define the curl of a

2D vect
or field F.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz
17.5

(Restrict 3D exercises to
first two components to get 2D exercises.)


Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Te
st

Questions 1, 4, 6, 7, and 8 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 5

(Restrict
3D examples to first two components to get 2D examples.)


Homework

Stewart Chapter 17.1: 21
-
26 (all), more TBD



Unit 4
.4
: Vector Fields
-

3D Gradient, Divergence, and Curl

Local
Objective



Define 3D vector field as the gradient of a scalar function f from
F from





.



Recognize when a 3D vector field F is or is not the gradient of a scalar function f.



Use the gradient operator to define the divergence and curl

of a vector field.



Recognize

how

the curl of a 2D vector field F can be viewed as the curl of a 3D
vector field with the z component function equal to zero.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and section
s.


Click here:

Interactive Quiz 17.5

(Intentionally used for both
2D and 3D formative assessment.)


Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 5, 10, 12, 13, 17, and 20 apply to this objective.

Learning Activity

PowerP
oint sli
des address
ing

the current objective.

Click here:

Chapter 17 Section 5

(Intentionally used for both 2D and 3D learning activity.)


Homework

Stewart Chapter 17.5: 1
-
8 (all),
12,
19
-
22 (all)




Unit 4
.5
: Vector Fields
-

Algebraic Properties of Gradient, Divergence, and Curl

Local
Objective



State the basic properties of the gradient, divergence, and curl operators and their
combinations.



Recognize that the curl of a gradient vector field is always zero.



Recognize that the divergence of a curl vector field is always zero.



Define the Laplacian operator using the gradient operator.

Formative Assessment

-

This quiz is correlated to the corres
ponding material drawn from a
supplementary textbook (Marsden).
Click here:

Algebraic Properties of Vector Fields Quiz





Summative Assessment

-

Students ar
e assessed over the entire unit.

Click here:

Vector Fields Test

Questions 7
-
11, 16
-
17, and 19 apply to this objective.

Learning Activity

The supplementary te
xtbook (Marsden) provides PowerP
oint presentations on each unit.



Click here:


(Marsden) Chapter 4 Section 3


and here:


(Marsden) Chapter 4 Section 4

(Intentionally used for both Algebraic and Geometric learning activities.)


Homework

Stewart Chapter 17.5: 23
-
32

(all)
, 39



Unit 4
.6
: Vector Fields
-

Geometric Properties of Gradient, Divergence, and Curl

Local
Objective



Interpret the divergence of a vector field in terms of the expansion or contraction of
the field geometry.



Interpret the curl of a vector field in terms of the

rotation (small paddle wheel)

about an axis at each point.

Formative Assessment

-

This quiz is correlated to the corresponding material drawn from a
supplementary textbook (Marsden).
Click here:

Geometric Properties of Vector Fields Quiz
.




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Vector Fields Test

Questions 12
-
13 and 27 apply to this objective.

Learning Activity

The supplementary te
xtbook (Marsden) provides PowerP
oint presentations on each unit.



Click here:


(Marsden) Chapter 4 Section 3


and here:


(Marsden) Chapter 4
Section 4

(Intentionally used for both Algebraic and Geometric learning activities.)


Homework

Marsden TBD



Unit 4
.7
: Vector Fields
-

Physical Interpretation

of Gradient, Divergence, and Curl

Local
Objective



Apply the gradient, divergence, and curl
appropriately in physical applications.



Use the properties of the gradient to determine temperature gradients.



Use the properties of the gradient to show that conservative fields, e.g., gravitational
fields, are gradients of scalar functions.



Use the prope
rties of the divergence and curl operators to represent, interpret, and
use Maxwell's Equations for electromagnetic fields.

Learning Activity

The supplementary textbook (Fleisch) provides an excellent online collection of podcasts,
problems, and
solutions, which corresponds quite nicely to the current learning activity since it is
designed for the student to gain experience using mathematics (already learned) in physical
applications. At this stage of vector calculus the student is prepared to add
ress only those
application problems involving the differ
ential form of Maxwell's Equati
ons, as indicated below.

Click here:


A Student's Guide to Maxwell's Equations
,

and here:


Problems 1.11
-
1.15
,

and
here:


Problem 2.6
,

and here:


Problems 4.6
-
4.10
.


Homework

Stewart Chapter 17.5: 37, 38, more TBD


Unit 4

Test


Final Exam Review


First Semester Final Exam



Unit 5
.1
: Multiple Integrals
-

Double Integrals

Local
Objective



Define the double integral of a function f

from







as the volume over a
rectangular region in the plane.



Compute the double integral as a double Riemann sum over a rectangular region.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.1



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 1 and 2 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 1



Homework


Stewart Chapter 16.1: 1
-
7 (odd)



Unit 5
.2
: Multiple Integrals
-

Iterated Integrals

Local
Objective



Define an iterated double integral using an iterated Riemann integral.



Use Fubini's theorem to show that iterated
double integral (in either order) is
equivalent to the double integral defined over a general region.



Compute double integral over general region using various iterated integrals.

Formative Assessment

-

Online interactive quizzes and tutorials correlated
to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.2



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 3
-
5 apply to this objective.

Learning Activity

PowerP
oint slides address
ing the current objective
.

Click here:

Chapter 16 Section 2



Homework

Stewart Chapter 16.2: 1, 3
-
27 (multiples of 3)



Unit 5
.3
: Multiple Integrals
-

Double Integrals Over a General Region

Local
Objective



Extend definition of double integral

to the volume over a

general region in the
plane.



Compute double integral over general region using a double Riemann sum over a
rectangular region containing the general region.

Formative Assessment

-

Online interactive

quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.3



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 6, 7, and 9 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.
Click here:

Chapter 16 Section 3



Homework

Stewart Chapter 16.3: 1, 3
-
27 (multiples of 3)



Unit 5
.4
: Multiple Integrals
-

Double Integrals in

Polar Coordinates

Local
Objective



Define an iterated double integral using an iterated Riemann integral in polar
coordinates.



Use Fubini's theorem to show that iterated double integral (in either order) in polar
coordinates is equivalent to the double int
egral defined over a general region in
polar coordinates.



Compute double integral over general region using various iterated integrals in
polar coordinates.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.4



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 8, 10, and 16 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 4



Homework

Stewart Chapter 16.4: 5
-
27 (
odd
)




Unit 5
.5
: Multiple Integrals
-

Applications of Double Integrals

Local Objective

Use double integrals
to compute total mass, total charge, center of mass, and moment of
inertia.


Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.



Click here:

Interactive Quiz 16.5

and here:

Interactive Quiz 16.6

This assessment may be
u
sed either as an homework quiz or as a small group quiz.




Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 11
-
16 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 5


Homework


Stewart Chapter 16.5: 1
-
19
(odd)



Unit 5.1
-
5.5

Test


Unit 5
.6
: Multiple Integrals
-

Triple Integrals

Local
Objective



Define the

triple integral of a function
f from







as the hyper
-
volume over a
rectangular

box in
F from




(a general region in



contained in a rectangular
box).



Compute

the triple

integral as a

triple Riemann sum over a rectangular

box in



(a
general region in


contained in a rectangular box).



Define an iterated

triple integral using an iterated triple Riemann integral.



Use

Fubini's theorem to show that iterated

triple integral (in

any order) is
equivalent to the

triple integral defined over a general region in


.



Compute

triple integral over general region in


using various iterated triple
integrals.



Interpret hyper
-
v
olume of triple integral with

(





)



as volume

of
a

general

region
in


.



Use triple integrals to compute center of mass and moments of inertia in


.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.7



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 1 and 2 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 6

(Note that
this

section number is different fro
m the quiz number due to different editions of the textbook.)

Homework


Stewart Chapter 16.6: 1
-
23 (odd), 27, 33



Unit 5
.7
:
Multiple Integrals
-

Triple Integrals in Cylindrical Coordinates

Local
Objective



Change back and forth from rectangular coordinates to cylindrical coordinates.



Identify geometrical settings that are natural for cylindrical coordinates.



Formulate and

compute triple integrals expressed in cylindrical coordinates.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.8



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Questions 18 and 19,
and here:

Chapter 16 Test

Question 15, all
apply to this objective. (Note that some of the topics in the textbook have been moved from
Chapter 13 to

Chapter 16.)

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 7

(Note that
this section number is diffe
rent fro
m the quiz number due to different editions of the textbook.)


Homework

Stewart Chapter 16.7: 1
-
21 (odd), 27



Unit 5
.8
: Multiple Integrals
-

Triple Integrals in

Spherical Coordinates

Local
Objective



Change back and forth from rectangular coordinates to spherical coordinates.



Identify geometrical settings that are natural for

spherical coordinates.



Formulate and

compute triple integrals expressed in

spherical coordinates.

Formative Assessment

-

Onlin
e interactive quizzes and tu
torials correlated to textbook
(Stewart)

c
hapters and sections.


Click here:

Interactive Quiz 16.8

(Intentionally used for both
cylindrical and spherical coordinates.)


Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 13 Test

Q
uestions 19
-
20,
and here:

Chapter 16 Test

Questions 13
-
15, all
apply to this objective. (Note that some of the topics in the textbook have been moved from
Chapter 13 to
Chapter 16.)

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 16 Section 8



Homework

Stewart Chapter 16.8: 1
-
25 (odd)




Unit

5
.9
: Multiple Integrals
-

Change of Variables

Local
Objective



Define a change of variable in




(


) as a transformation T from







(






) such that T is a 1
-
1 continuously differ
enti
able function.



Use the Jacobian matrix
determinant corresponding to a change of variable
transformation T to rewrite and compute double and triple integrals.



Interpret the change from rectangular coordinates to polar coordinates in double
integrals as a change of variable using an appropriate J
acobian matrix determinant.



Interpret the change from rectangular coordinates to

cylindrical or
spherical

coordinates in

triple integrals as a change of variable using an appropriate
Jacobian matrix determinant.

Formative Assessment

-

Online interactive q
uizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 16.9



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 16 Test

Questions 11, 16, and 18
-
20 apply to this objective.

Learning Activity

PowerP
oint slides
address
ing

the current objective.

Click here:

Chapter 16 Section 9


Homework


Stewart Chapter 16.9: 1
-
6 (all), 7
-
23 (odd)



Unit 5.6
-
5.9

Test



Unit 6
.1
: Vector
Calculus

-

Line Integrals

Local
Objective



Define path (line) integral along a space curve

in



(


)
.



Interpret path (line) integral as a generalization of an arc length integral.



Define the work done along a curve in terms of a path (line) integral.



Compute

path (line) integrals using various techniques of integration.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.2



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 1
-
3 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17

Section 2



Homework

Stewart Chapter 17.2: 1
-
30

(multiples of 3)



Unit 6
.2
: Vector Calculus

-

Fundamental Theorem of Line Integrals

Local
Objective



State the Fundamental Theor
e
m of line integrals using the gradient operator and
the dot product.



Interpret

the Fundamental Theor
e
m of line integrals as a generalization of the
Fundamental Theorem of Calculus.



Use the Fundamental Theor
e
m of line integrals to compute path (line) integrals of
vector fields that are gradients of scalar fields (conservativ
e vector fields)

and
recognize the path independence.



For vector fields that represent physical forces, interpret path integrals as the work
done along the path.



Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stew
art)

chapters and sections.


Click here:

Interactive Quiz 17.3



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 4
-
8 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 3




Homework

Stewart Chapter 17.3: 1
-
21 (
odd
)



Unit 6
.3
: Vector Calculus

-

Green's Theorem

Local
Objective



State Green's Theorem relating the path
(line) integral around a simple closed curve
to the double integral over the enclosed region.



Interpret

Green's

Theorem

as a generalization of the Fundamental Theorem of
Calculus for double integrals.



Use Green's Theorem to simplify the computation of a di
fficult path (line) integral
using a double integral.



Use Green's Theorem to simplify the computation of a difficult

double integral using
a

path (line) integral.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.4



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 9
-
11 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 4


Homework


Stewart Chapter 17.4: 3
-
19 (odd)



Unit 6
.4
: Vector Calculus

-

Second Version of Green's

Theorem

Local
Objective



Restate Green's Theorem in terms of the curl and divergence operators.



Apply this form of

Green's Theorem to flows of (incompressible) vector fields.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.5



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 12
-
14 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 5



Homework

Stewart Chapter 17.5:
2
-
28 (even
-
review), 33
-
35 (all)


Unit 6.1
-
6.4

Test



Unit 6
.5
: Vector Calculus

-

Parametric Surfaces

Local
Objective



Write the parametric equations of a surface in



using a smooth mapping from








.



Interpret the parameterization of a surface geometrically as a function that maps a
2D (flat) region of the plane to a (curved) surface in 3D space.



Use technology to visualize parameterized surfaces.



Use double integrals to compute the area of parameterized surfaces.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.6



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 9 and 14
-
16 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 6



Homework

Stewart Chapter 17.6
A
:
1,
3
-
27

(
multiples of 3
)


Stewart Chapter 17.6B: 33
-
47 (odd)





Unit 6
.6
: Vector Calculus

-

Surface Integrals

Local
Objective



Define a surface integral
for a scalar field f mapping







,

where the surface S is
contained in the domain of f and S is parameterized.



Compute surface integrals using appropriate parameterizations and double
integrals.



Compute the

surface integral of a vector field F over a surface S using the normal
component of F with respect to S.

Formative Assessment

-

Online interactive quizzes and tu
torials correlated to textbook
(Stewart)

c
hapters and sections.


Click here:

Interactive Quiz 17.7



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 16 and 18 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 7



Homework

Stewart Chapter 17.7: 3
-
27 (multiples of 3)



Unit 6
.7
: Vect
or Calculus

-

Stokes

Theorem

Local
Objective



State Stoke
s

Theorem for a smooth vector field

F on


,

which relates the path (line)
integral of the tangential component of F around a simple closed boundary

curve C
of a surface S to the surface integral of the normal component of the curl of F over
the enclosed surface S.



Interpret

Stokes

Theorem

as a ge
neralization of

Green's Theorem.



Use

Stokes

Theorem

to simplify the computation of a difficult path (line) integral for
the vector field F.



Use

Stokes

Theorem

to simplify the computation of a difficult

surface integral of the
flux of the vector field F
through the surface.



Define the circulation of a vector field F abo
ut a closed curve and use Stoke
s
Theorem to relate it to the

magnitude of the normal component of the curl of F.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.8



Summative Assessment

-

Studen
ts are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 10 and 16 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 8



Homework

Stewart Chapter 17.8: 3
-
27 (multiples of 3)



Unit 6
.8
: Vector Calculus

-

Divergence Theorem

Local
Objective



State

the Divergence Theorem for a smooth vector field

F on


,

which relates
the

surface integral of the

normal component of F over the surface S, e.g., the
boundary surface of a region

E of




, to the

triple integral (volume
integral) of the
divergence

of F over E.



Interpret the Divergence Theorem as a generalization of

Green's Theorem.



Use

the Divergence Theorem to simplify the computation of a difficult surface
integral for the vector field F.



Use

the Divergence Theorem to
simplify the computation of a difficult

volume
integral for the vector field F.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 17.9



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 17 Test

Questions 17 and 20 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 17 Section 9



Homework


Stewart Chapter 17.9: 3
-
27 (multiples of 3)





Unit 6
.9
: Vector Calculus

-

Physical Applications of Path, Surface, and Volume Integrals

Local
Objective



Apply path, surface, and volume integrals and their related
theorems to problems in
fluid dynamics and electrodynamics.



Use surface and volume integrals and their related theorems to state integral forms
of Maxwell's Equations for electromagnetic fields.

Learning Activity

The supplementary te
xtbook (Marsden) provi
des PowerP
oint presentations on each unit.



Click here:

(Marsden) Chapter 8 Section 5


Homework

TBD


Unit 6.5
-
6.9

Test



Unit 6
.10
: Vector Calculus

-

Introduction to Differential Forms

Local
Objective



Re
-
interpret differentials and their products in terms

of

1
-
forms, 2
-
forms, and 3
-
forms.



Compute exterior products of differential forms.



Restate Stokes

Theorem in terms of differential forms.

Learning
Activity

The supplementary te
xtbook (Marsden) provides PowerP
oint presentations on each unit.



Click here:

(Marsden) Chapter 8 Section 6



Homework

TBD



Unit 6
.11
: Vector Calculus

-

Introduction to the Gauss
-
Bonnet Theorem

Local
Objective



Define the shape operator and Gaussian curvature of a smooth, orientable

patch in


.



Compute the shape operator and Gaussian curvature of basic geometrical

shapes in


.



Redefine Gaussian curvature in terms of 2
-
forms for geometrical (metric) surfaces
in


.



State the Gauss
-
Bonnet Theorem which relates the total Gaussian Curvature of a
compact, orientable, geometrical (metric) surface to its Euler characteristic wi
th
respect to any rectangular decomposition of the surface.

Learning Activity

The supplementary te
xtbook (Marsden) provides PowerP
oint presentations on each unit.



Click here:

(Marsden) Chapter 7 Section 7



Homework

TBD



Unit 7
.1
: Second
-
Order Differential Equations
-

Second
-
Order Linear Equations

Local
Objective



Construct the
solution of a linear homogeneous differential equation by finding a
basis for the solution space of the

corresponding operator

polynomial.



Solve

linear homogeneous differential equations satisfying various initial and
boundary conditions.

Formative Assess
ment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 18.1



Summative Assessment

-

St
udents are assessed over the entire unit.

Click here:

Chapter 18 Test

Questions 1
-
2 and 4
-
9 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 18 Section 1



Homework

Stewart Chapter 18.1: 3
-
30

(multiples of 3)



Unit 7
.2
: Second
-
Order Differential Equations
-

Non
-
Homogeneous Linear Equations

Local
Objective



Use the method of undetermined coefficients to solve

linear inhomogeneous
differential equations satisfying various initial and boundary conditions.



Use

the method of

variatio
n of parameters

to solve

linear
inhomogeneous

differential equations

satisfying various initial and boundary
conditions.



Interpret both methods (Method of Undetermined Coefficients and Method of
Variation of Parameters) in terms of finding a basis

for the
solution space of an
appropriately chosen operator polynomial.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook

(Stewart)

chapters and sections.


Click here:

Interactive Quiz 18.2



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 18 Test

Questions 3 and 10
-
14 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 18 Section 2


Homework


Stewart Chapter 18.2: 3
-
27 (multiples of 3)



Unit 7
.3
: Second
-
Order Differential Equations
-

Physical Applications

Local Objective



Apply the methods

used to solve linear differential equation to represent and solve
physical problems involving simple harmonic motion, including those with various
forms of damped vibration.

Formative Assessment

-

Online interactive quizzes and tutorials

correlated to textbook
(Stewart)

chapters and sections.


Click here:

Interactive Quiz 18.3



Summative Assessment

-

Students are assessed over the entire unit.

Clic
k here:

Chapter 18 Test

Questions 15
-
18 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 18 Section 3


Homework


Stewart Chapter 18.3: 1
-
17 (odd)



Unit 7
.4
: Second
-
Order Differential Equations
-

Series Solutions

Local
Objective



Use power
series

methods to solve linear differential equations.



Extend power series methods to

solve nonlinear differential equations.

Formative Assessment

-

Online interactive quizzes and tutorials correlated to textbook
(Stewart)

chapters and sections.


Click her
e:

Interactive Quiz 18.4



Summative Assessment

-

Students are assessed over the entire unit.

Click here:

Chapter 18 Test

Questions 19
-
20 apply to this objective.

Learning Activity

PowerP
oint slides address
ing

the current objective.

Click here:

Chapter 18 Section 4



Homework

Stewart Chapter 18.4: 1
-
11 (odd)


Final Exam Review


Second

Semester Final Exam