Math 1572H Honors Calculus
Spring Semester 2006, 4 credits
Lecture:
Place: CSci 3-115
Time: 10:10-11:00 MWF
Text: G.F. Simmons, Calculus with Analytic Geometry, 2nd
ed., McGraw-Hill
Instructor: Willard Miller
Office: Vincent Hall 513, 612-624-7379, miller@ima.umn.edu, miller@math.umn.edu,
www.ima.umn.edu/~miller
Office hours: 11:15-12:05 M, 13:25-14:15 W, 9:05-9:55 F, or by appointment
Discussion Sections:
011: 9:05-9:55 am TTH, VinH 206, TA: Ryan Gantner,
Office: Vincent Hall 505, 612-634-0518; gantner@math.umn.edu
012: 10:10-11:00 am TTH,
VinH 311, TA: Ryan Gantner
Course Content:
Most of this material will be taken from Chapters 10 - 19 of the text. I will also include some material in the lectures that is not in the book, particularly applications to rocket science (satellite and planetary orbits, impulse maneuvers, etc.).
Syllabus (from
the text):
| Sections |
Topics |
| 10.1-10.9 |
Methods of integration |
| 11.1-11.3 |
Centroids, Center of mass
|
| 12.1-12.4 |
Indeterminant forms, L'Hospital's
rule, improper integrals |
| 13.1-13.8 |
Infinite series |
| 14.1-14.6 |
Power series, Taylor's formula |
| 16.1-16.4 |
Polar coordinates revisited |
| 17.5-17.6 |
Curvature and normals, Tangential
and normal components of acceleration |
| 18.6-18.7 |
Quadric surfaces, Cylindrical
and spherical coordinates |
| 19.1-19.5 |
Partial derivatives, Tangent
planes, Directional derivatives and gradient |
| 19.7 |
Maximum and minimum problems
in several variables |
| Date |
Sections |
Homework (due Thursday of following
week) Turn in starred problems. |
| Tu 1/17 |
10.1, 10.2 |
|
| W 1/18 |
10.3, 10.4 |
|
| F 1/20 |
10.4, 10.5 |
|
| M 1/23 |
10.6 |
|
| W 1/25 |
10.7 |
|
| F 1/27 |
10.8 |
|
| M 1/30 |
10.9 |
|
| W 2/1 |
11.1, 11.2, |
|
| F 2/3 |
11.3, Rocket Science |
|
| M 2/6 |
12.1, 12.2 |
|
| W 2/8 |
12.3 |
|
| F 2/10 |
12.4 |
|
| M 2/13 |
Rocket Science |
|
| W 2/15 |
Review |
|
| F 2/17 |
Midterm I |
|
| M 2/20 |
13.1, 13.2 |
|
| W 2/22 |
13.3 |
|
| F 2/24 |
13.4 |
|
| M 2/27 |
13.5, 13.6 |
|
| W 3/1 |
13.7 |
|
| F 3/3 |
13.8 |
|
| M 3/6 |
Rocket Science |
|
| W 3/8 |
14.1, 14.2 |
|
| F 3/10 |
14.3 |
|
| 3/13-3/17 |
Spring Break! |
|
| M 3/20 |
14.4 |
|
| W 3/22 |
14.5 |
|
| F 3/24 |
14.6 |
|
| M 3/27 |
16.1, 16.2 |
|
| W 3/29 |
Review |
|
| F 3/31 |
Rocket Science |
|
| M 4/3 |
Midterm II |
|
| W 4/5 |
16.1, 16.2 |
|
| F 4/7 |
16.4 |
|
| M 4/10 |
17.5, 17.6 |
|
| W 4/12 |
18.6, 18.7 |
|
| F 4/14 |
19.1 |
|
| M 4/17 |
19.2 |
|
| W 4/19 |
19.3 |
|
| F 4/21 |
19.4, 19.5 |
|
| M 4/24 |
19.5, 19.7 |
|
| W 4/26 |
Review |
|
| F 4/28 |
Midterm III |
|
| M 5/1 |
19.7 |
|
| W 5/3 |
Review |
|
| F 5/5 |
Review |
|
| M 5/8 |
Final Exam |
1:30-4:30 pm, Akerman Hall
209 |
I will move rapidly through
the standard material and go more deeply into a few particular applications,
and introduce some special material not in the text. One area will be celestial
mechanics (e.g., satellite and planetary orbits, stability of orbits).
I will also talk about stability and control of general dynamical systems
that arise in the economic and biological sciences, as well as the physical
sciences. I will post special topics and demos on the course website to
help illustrate these and other course topics.
Course Assessment
There will be three full-period mid-term exams,
to be held on Friday February 17, Monday April 3 and Friday April
28. The final exam will be held 1:30-4:30
Monday, May 8. It will not be held in the usual classroom, but in
a different room to be announced towards the end of the semester. You will
also have homework and quizzes organized by the TA in recitations. Your
final grade will be made up of homework and quizzes 18%, mid-term exams
14% each, a small-group project 5% and final exam 35%. The project will
be related to rocket science (i.e., orbit determination, stability of orbits,
etc.).
Homework
Homework will be due every Thursday at the beginning of class. Only
the starred problems on the assignment guide should be turned in. Since
relatively few of the homework problems will be turned in, I expect that
some care be taken in the presentation of the homework. Please see the section
labeled "expectations of written work". There will be 13 regular homework
assignments, the first of which is due in week 2. The lowest homework
grade will be dropped. In addition, there will be a "bonus" homework assignment,
which will be due in week 15. Since this is a short assignment (only 3
starred problems), any points accumulated in this assignment will simply
be added to your homework score. The 12 homeworks which count, plus the
bonus homework, will comprise 9% of the course grade. Since the schedule
of assignments and content coverage is likely to change, I reserve the right
to change this homework policy as is appropriate, provided I give plenty of
notice and obtain the consent of the class.
Late homework will not be accepted without prior consent of the TA.
If you must miss a Thursday discussion for some reason, you must turn
in the homework before the time it is due. You will receive no assistance
privately from the TA on the starred problems. That is, I will not talk
about the starred problems with you in office hours; I will instead work
on a similar problem. I may work on starred problems in class (so everyone
has equal access), but I would rather elect to work on similar problems.
You are encouraged to work with your classmates on all of the homework problems,
but every student must write up their own final draft of the assignment.
Answers to un-starred, even-numbered problems will be posted on the course
website by either the TA or the professor.
Recitation Quizzes
There will be a quiz every Thursday at the beginning of recitation,
with some exceptions*. The quiz will take approximately 15 minutes. If
you are late to class, then you will have less time to do the quiz. There
will be 10 quizzes this semester, with the lowest quiz grade dropped. No
makeup quizzes will be offered, even for "good" excuses. The 9 quizzes
(10 minus 1 dropped score) will count for 9% of the total course grade.
Unless otherwise noted beforehand, any type of calculator will be allowed
to do quiz work. Quiz problems may be taken from the homework set. Quiz
solutions will be posted on the course website.
*The weeks when there will be no quiz are weeks 1, 5, 10, 14, and
15. These are the weeks of the midterm exams, final exam, and the first
week of class.
Absence from exams
Missing a midterm is permitted only for the most compelling reasons.
Except in extraordinary situations, you should obtain permission from the
professor to miss an exam in advance; otherwise you will be awarded
a 0. If you are excused from taking a midterm, your course grade will
be determined by giving extra weight to the final exam. No make-up exams
or quizzes will be given. Except in extremely exceptional situations, all
students missing the final exam will fail the course. Don't bother to obtain
permission to miss a quiz: your lowest quiz score will not be counted.
Attendance
Students are expected to attend all lectures and recitations.
Attendance may be checked and included in the grade line.
Expectations of written work
In a number of cases in
the homework problems and the questions in the exams you will not get full
credit if you simply write down the correct answer. To get full credit
you will need to write an explanation of how you got your answer. Where
explanations need to be given, these should be written out in sentences,
i.e. with verbs, capital letters at the beginning, periods at the end, etc.
and not in an abbreviated form. You are encouraged to form study groups.
However everything to be handed in must be written up in your own words.
If two students hand in identical assignments, they will both receive no
credit.
We expect homework to be legible and to follow professional standards.
In addition to the expectations above we expect the following:
*You should use a stapler to attach the papers (i.e., do not use
paper clips and do not curl the paper from the corner.)
*You should leave margins and space between problems. Neatness and
logical organization is required.
*Your name and section number should be clearly legible on the top
of the front page of each homework assignment and quiz.
Computers and Calculators
Everyone should have a graphing calculator. Calculators
will be allowed on all quizzes and exams. Computers (e.g., laptops) may
not be used on quizzes and exams. No cell phones or other communication
devices may be used during exams.
Incompletes
These will only be given in exceptional circumstances.
A student must have satisfactorily completed all but a small portion of
the work in the course, have a compelling reason for the incomplete, and
must make prior arrangements with the professor for how the incomplete
will be removed, well before the end of the quarter.
University Grading Standards
A achievement that is outstanding relative to the level necessary
to meet course requirements.
B achievement that is significantly above the level necessary
to meet course requirements.
C achievement that meets the course requirements in every
respect.
D achievement that is worthy of credit even though it fails
to meet fully the course requirements
S The minimal standard for S is to be no lower than C-. The
instructor or department must inform the class of this minimal standard
at the beginning of the course.
F (or N) Represents failure (or no credit) and signifies that
the work was either (1) completed but at a level of achievement that is
not worthy of credit or (2) was not completed and there was no agreement
between the instructor and the student that the student would be awarded
an I.
I (Incomplete) Assigned at the discretion of the instructor
when, due to extraordinary circumstances, e.g. hospitalization, a student
is prevented from completing the work of the course on time. Requires
a written agreement between instructor and student.
Academic Dishonesty.
Academic dishonesty in any portion of the academic work for a course shall
be grounds for awarding a grade of F or N for the entire course.
Credits and Workload Expectations. For undergraduate courses,
one credit is defined as equivalent to an average of three hours of learning
effort per week (over a full semester) necessary for an average student
to achieve an average grade in the course. For example, a student taking
a three credit course that meets for three hours a week should expect to
spend an additional six hours a week on course work outside the classroom.
******************************************************************************************************
Brief solutions
to 1571H final exam questions
*******************************************************************************************************
Newton's Method and the Mean Value Theorem
Extended Mean Value
Theorem and L'Hospital's Rule
Graphs of
some Taylor polynomial approximations of sin(x), -4 < x < 4.
Note that the Taylor polynomial
T_19(x) is such a good approximation that the graphs can't be distinguished
in the interval -4 < x < 4.
The Alternating Series Estimation Theorem with examples