Course: MATH 219 Multivariate Calculus Term: Fall 2007 Meets: MWF 10:40 - 11:50
Instructor: Craig Kalicki Office: H-284
E-mail: craig.kalicki@briarcliff.edu Phone: 279-5541
Text: Stewart, Calculus Early
Transcendentals, Fifth Edition, Thomson Brooks/Cole, ©2003
ISBN 0-534-39321-7
Goals of course:
This
is the third course in the calculus sequence intended for students in
mathematics, the physical sciences,
and
pre-engineering. The emphasis is on
concepts and applications in three-dimensional space. Students
should
expect to
1)
gain further appreciation of calculus as an organized body of
mathematical tools with numerous
applications in the sciences.
2)
develop some of the mathematical skills needed to understand and apply
models involving the concepts
of multivariate calculus.
3)
gain further experience with the use of technology as a tool for
exploring and applying mathematics in
higher dimensions.
Prerequisites:
Students in
this course should have passed MATH 218 Calculus II or an equivalent course at
another institution.
Expectations of students:
1) Attend class on a regular basis. Three or more unexcused absences should be
considered excessive.
2) Read and review the text as needed, paying
particular attention to terminology and examples. You may want
to take some notes in class but be
aware that most of the material you are responsible for is discussed in
the text.
3) Come to class prepared to ask questions,
participate in discussions, and present solutions of assigned
problems. Doing assignments with others in the course
is encouraged.
4) Make use of your instructor's office
hours. Ask for help whenever
difficulties arise or you feel the need for
advice or encouragement.
5) Hand in reasonably complete homework
assignments. Credit will be given for
handing in assignments and
selected problems will be graded. Answers to odd-numbered exercises are in the
back of the text.
Assignments are to be handed in on the
dates due. No late work will be accepted except in cases of
serious illness or family
emergency.
6) Show evidence of learning on exams. Exams will be thorough and sufficient study
time must be allowed.
Unexcused absence from an exam will
result in an automatic grade of zero for that exam.
Grading:
|
Two exams @ 25% |
50% |
|
A = 100 - 93 |
C+ = 76 - 74 |
|
Final exam |
30% |
|
A- = 92 - 90 |
C = 73 - 67 |
|
Assignments |
20% |
|
B+ = 89 - 87 |
D+ = 66 - 64 |
|
|
|
|
B = 86
- 80 |
D = 63 - 55 |
|
Total |
100% |
|
B- = 79 - 77 |
|
Grading rubric:
The
grading rubric below will be used to assess written work, including text
assignments and exam questions.
|
Level |
Characteristics |
|
4 |
Solution
is correct and clearly stated. |
|
3 Good |
Solution
is substantially correct. |
|
2 Adequate |
Solution
is flawed but basically correct. |
|
1 Minimal |
Solution
is attempted but significant errors occur. |
|
0
Unacceptable |
Solution
is omitted or an answer is given with no supporting evidence. |
Technology:
Each student
should have a graphing calculator available for use during class and
exams. Recommended
models are
the TI 84+, TI-86 or TI-89. The software
Derive™ 6 is installed on the Briar Cliff network and may
be used when
doing assigned problems.
Learning
outcomes:
The
specific learning outcomes for this course are listed below. Assessment of the degrees to which these
outcomes
have been achieved will be done via written exams and homework assignments.
Students
who have completed MATH 219 will be able to
1)
perform vector operations in space.
2)
describe algebraically lines and planes in space.
3)
identify and describe elementary types of surfaces in space.
4)
analyze the behavior of vector functions.
5)
apply the calculus of vector functions.
6)
describe the behavior of functions of two variables using surfaces and
contour maps.
7)
compute limits and determine continuity for functions of two variables.
8)
understand, compute, and interpret partial derivatives.
9)
find linear approximations for functions of two variables.
10)
compute and apply directional derivatives and gradients.
11)
determine local extreme values and saddle points for functions of two
variables.
12)
understand the concepts of the double and the triple integral.
13)
compute the value of a double integral using iterated integrals.
14)
apply the double integral to problems involving volume and center of
mass.
15)
describe vector fields in the plane and in space.
16)
understand, compute, and apply line integrals in the plane and in space.
17)
identify and apply conservative vector fields.
Course
outline:
Ch 12 Vectors and the Geometry of Space [5 classes]
Three-dimensional coordinate system / vectors in space / dot products /
cross products /
equations of lines and planes in space / cylinders and quadric surfaces.
Ch 13 Vector Functions [5 classes]
Vector functions /
curves in space / derivatives and
integrals of vector functions / arc
length and
curvature
/ motion in space.
Ch 14 Partial Derivatives [7 classes]
Functions of several variables / limits and continuity / partial derivatives /
tangent planes / linear
approximation / chain rules
/ directional derivatives and gradients / maxima and minima..
Ch 15 Multiple Integrals [5 classes]
Double integrals / iterated integrals / double integrals in polar form / moments and center of mass /
surface area /
triple integrals.
Ch 16 Vector Calculus [4 classes]
Vector
fields /
line integrals / work
/ conservative fields and path
independence.
Ó2007 by Craig
Kalicki PhD,