Professor: Jeff Johannes
Section 1
MWF 11:30a-12:20p South 328
Office: South
326A
Telephone: 245-5403
Office Hours Open Classroom Time with
Jeff: , and by appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page: https://tildesites.geneseo.edu/~johannes/
Textbooks
Second Year Calculus, David M. Bressoud
Course Goals
- Discuss the fundamentals of vector calculus from a more
advanced perspective (differential forms, gradient, directional
derivative, divergence, curl, Laplacian, and differential forms)
- Place them in the physical context for which they were
initially developed and learn the story of their creation.
- Read a serious mathematics book from page 1 to page
360.
Learning Outcomes
Math 350 - Upon successful completion of Math
350 - Vector Analysis, a student will be compute and analyze:
- Scalar and cross product of vectors in 2 and 3 dimensions
represented as differential forms or tensors,
- The vector-valued functions of a real variable and their
curves and in turn the geometry of such curves including
curvature, torsion and the Frenet-Serre frame and intrinsic
geometry,
- Scalar and vector valued functions of 2 and 3 variables and
surfaces, and in turn the geometry of surfaces,
- Gradient vector fields and constructing potentials,
- Integral curves of vector fields and solving differential
equations to find such curves,
- The differential ideas of divergence, curl, and the Laplacian
along with their physical interpretations, using differential
forms or tensors to represent derivative operations,
- The integral ideas of the functions defined including line,
surface and volume integrals - both derivation and calculation
in rectangular, cylindrical and spherical coordinate systems and
understand the proofs of each instance of the fundamental
theorem of calculus, and
- Examples of the fundamental theorem of calculus and see their
relation to the fundamental theorems of calculus in calculus 1,
leading to the more generalised version of Stokes' theorem in
the setting of differential forms.
Grading
Your grade in this course will be based on
problem sets, three in-class quizams, two take-home exams, and a
final examination. Each of those aspects will be worth 1/4 of
your grade and each component of each aspect will be equally
weighted.
Problem sets will consist of questions related to
material presented in the previous two weeks. They will be due
two weeks after assigned. Before these papers are handed
in, I strongly suggest discussing them with me and others
outside of class. These discussions will be graded on a ten
point decile scale based on completeness, accuracy, and writing.
These problems will be evaluated as follows.
0 Missing
3 Question copied, nothing written
6 Something written that appears that it was only
written to take up space
7 Substantially incomplete. Something written,
but does not really answer the main questions. Major errors.
Very poor writing
8 Mostly complete, maybe a few minor errors
9 Complete, no errors, some personal insight,
well-written
10 Wonderful
We will discuss these problem sets in detail on
the day they are due. Therefore no late problem sets will be
accepted.
Solutions and Plagiarism
There are plenty of places that one can find all
kinds of solutions to problems in this class. Reading them and
not referencing them in your work is plagiarism, and will be
reported as an academic integrity violation. Reading them and
referencing them is not quite plagiarism, but does undermine the
intent of the problems. Therefore, if you reference solutions
you will receive 0 points, but you will *not* be reported for an
academic integrity. Simply - please do not read any solutions
for problems in this class.
Opening
Meeting
Students
will earn two extra points on the first problem set by visiting
office hours during the first two weeks of classes, i.e. no later
than 4 September.
Quizams
Quizams are like long quizzes or short
exams. You will have 20 minutes to complete them. They
will focus on computational fluency with material since the last
quizam.
Take Home Exams
The take home exams will be more involved than
quizams and less than problem sets. They are due the class-day
after they are distributed. You may not consult with any other
person, and any resource other than your notes and your
textbook. If you do consult with other sources, you will be
failed in this course and reported to the Dean of Students for a
violation of academic integrity. It is responsible to plan in
advance to allocate time for them, and not unreasonable to study for
them.
Final Examination
You will have two options for a final
examination. You may take a cummulative three hour final
examination (more involved than a quizam and less involved than a
take-home exam). Your second option is a cummulative take-home
exam that will be distributed at the last day of class and due by
the end of the final examination period (more involved than
the other take home exams).
Feedback
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for
how the course is running. Remember, the sooner you tell me
your concerns, the more I can do about them. I have also
created a web-site
which
accepts anonymous comments. If we have not yet discussed
this in class, please encourage me to create a class code.
This site may also be accessed via our
course page on a link entitled anonymous
feedback. Of course, you are always welcome to approach
me outside of class to discuss these issues as well.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the opportunity to make
up missed work. You are responsible for notifying me no later
than September 4 of plans to observe the holiday.
Tentative Schedule subject to change
Date
Topic
Assigned Due
August
24 Introduction, §1.5 Kepler's first
26 §1.5 Gravity
28
1.5 / 3.1
31
3.1
September 2 3.1
PS 1
4
3.3
9
3.3
11 3.3
14
4.1 / 4.2
16
4.2
18
Discuss problem set
PS 2
PS 1
21
4.4
23 4.4
25
4.6
Quizam 1 (material thru PS1)
28
4.6
30
4.7, 5, 6, 7
October
2 Discuss problem set
PS
3 PS 2
5
8.1 / 8.2
7
8.2
Take Home Exam 1 (material thru
PS2)
9
8.4
THX1
14
8.4
16
8.5
19
Discuss problem set
PS4 PS 3
21 10.1
23 10.1
26 10.2
Quizam 2 (material
thru PS3)
28 10.2
30 10.4
November
2 Discuss problem set
PS
5 PS 4
4
10.4
6
10.6
9
10.6
Take Home Exam 2 (material
thru PS4)
11 10.6
THX2
13
10.7
16 Discuss
problem set
PS 6
PS 5
18 10.9
20
11.1
23 11.2
Quizam
(material thru PS5)
30 11.3
December 2
11.5
4 Discuss
problem
set
PS 6
7
review
Take-home final
Wednesday
9 12N - 2:30p Final Examination
Take-home
Final