Math 1572H
Honors Calculus
Spring Semester 2007, 4 credits
Lecture:
Place: VinH 16
Time: 10:1011:00 MWF
Text: G.F. Simmons, Calculus with Analytic Geometry, 2nd
ed., McGrawHill
Instructor: Willard Miller
Office: Vincent Hall 513, 6126247379, miller@ima.umn.edu,
miller@math.umn.edu, www.ima.umn.edu/~miller
Office hours: 13:2514:15 M, 9:059:55 W,
12:2013:10 F,
or by appointment
Discussion Sections:
011: 9:059:55 am TTH,
VinH 311, TA: Hazem Hamdan,
Office:
VinH 360,
(612) 6254392, hamdan@math.umn.edu
Office hours: 14:3016:30 MW
012: 10:1011:00
am TTH, LindH 340, TA: Hazem Hamdan, Office:
VinH 360,
(612) 6254392, hamdan@math.umn.edu
Office hours: 14:3016:30 MW
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 
10.110.9 
Methods of integration 
11.111.3 
Centroids, Center of
mass 
12.112.4 
Indeterminant forms,
L'Hospital's rule, improper integrals 
13.113.8 
Infinite series 
14.114.6 
Power series, Taylor's formula 
16.116.4 
Polar coordinates revisited 
17.517.6 
Curvature and normals,
Tangential and normal components of acceleration 
18.618.7 
Quadric surfaces, Cylindrical
and spherical coordinates 
19.119.5 
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 1/16 
10.1, 10.2 
10.2 3*,
4,18,19,22*,31 
W 1/17 
10.3, 10.4 
10.3
6,7,8,9*,
12*, 15,21 10.4 5.6*, 12 
F 1/19 
10.4, 10.5 
10.4 14*,
16,18
10.5 2,4,6,10*,14* 
M 1/22 
10.6 
10.6
1b,6,10,11,15*,16, 20,21, 22*, 24 
W 1/24 
10.7 
10.7 3,
5*, 7*, 8, 9, 12, 14*, 17, 18* 
F 1/26 
10.8 
10.8 12*,
17,
26, 39*, 43*, 96, 102 
M 1/29 
10.9 
10.9
1*,3,8* 
W 1/31 
11.1, 11.2, 
11.2
2*,3, 9*,16

F 2/2 
11.3, Rocket Science 
11.3
1a,2*(just do volume problem)
Rocket Science 3. Problems
1,2*,3,4,5*,6, 7(2)*,7(3) 
M 2/5 
12.1, 12.2 
12.2
6, 7, 8, 14*, 21, 22* 
W 2/7 
12.3 
12.3
2*, 5, 7, 10, 20*, 24, 30, 34*, 36 
F 2/9 
12.4 
12.4
2, 4*, 8, 10*, 13, 17, 23, 24a, 24b*, 24c, 24d.
Page
426 115*, 118 
M 2/12 
Rocket Science 
Rocket Science 4.
Problems 1*,2,3*,4,5*,6 
W 2/14 
Review 

F
2/16 
Midterm I 
Covers material through
section 12.4 
M 2/19 
13.1, 13.2 
13.2
1b*, 1d, 1e, 1g, 1i, 9a*, 10a*, 14 
W 2/21 
13.3 
13.3
2b, 2i,
2l*, 5b, 5e*, 5f, 5g*, 5h, 10a, 12 
F
2/23 
13.4 
13.4
1, 2, 2a*, 2b*, 2c*, 2e* 3c, 3d, 6, 8* 
M 2/26 
13.5, 13.6 
13.5
1, 1e*,
1f*, 1h, 2, 3*, 4*, 6, 7, 9*, 11, 15, 18, 27* 13.6
1, 4*,
7, 8* 
W 2/28 
13.7 
13.7
2*, 4*,
6, 8, 9, 10* 
F
3/2 
13.8 
13.8
4, 6, 8, 18*, 20*, 23*, 24*, 25, 26 
M 3/5 
Rocket Science 
Rocket Science 5.
Problems 1*,2*,4*,5,8 
W 3/7 
14.1, 14.2 
14.2
2*, 4, 6*, 14, 16, 18, 22*, 24, 26* 
F
3/9 
14.3 
14.3
1, 1a*,
2, 3, 3a*, 4 
3/123/16 
Spring Break! 

M 3/19 
14.4 
14.4
4, 4h*,
5, 6, 7, 8*, 12*, 13, 14, 15, 18a* 
W 3/21 
14.5 
14.5 1*,
2, 4, 9*, 10, 12, 15 
F
3/23 
14.5 

M 3/26 
Rocket Science 
Rocket Science 6. Problem 1*, Rocket Science 3. Problem 8* 
W 3/28 
Review 

F
3/30 
Rocket Science 
Rocket Science Project:
Loiterer II 
M
4/2 
Midterm II 
Covers material through
section 14.5 
W
4/4 
16.1, 16.2 
16.1 1ab,
2cd, 7, 8*, 9b
16.2 2a, 4cefglm, 4k*, 4n*, 5fg, 5h*,
6, 6e*, 10b* 
F
4/6 
16.4 
16.4
1,2*,3a,c*,e, 5*,8,15 
M 4/9 
17.5, 17.6 
17.5
1c*,e, 2b,d* 7,9*
17.6 2*,3,4*,6 
W
4/11 
18.6, 18.7 
18.6
1*,2,15*,19,22*
18.7 1a*d,
2bc*,3ad,5*,13,14* 
F
4/13 
19.1 
19.1 2, 4,
5, 8, 10*, 13*, 14, 15, 17, 18, 20*, 22*, 24* 
M
4/16 
19.2 
19.2 6,
10, 16, 20*, 21, 26*, 31* 
W 4/18 
19.3 
19.3 2,
4*, 8,
10*, 15 
F
4/20 
19.4, 19.5 
19.5 1ab,
2, 2b*, 3a*, 5*, 8 
M
4/23 
19.5, 19.7 
19.7 10*,
11, 13*, 15*, 18, 22 
W
4/25 
Review 

F
4/27 
Midterm III 
Covers material through
section 19.3 
M
4/30 
19.7 

W
5/2 
Review 

F
5/4 
Review 

M
5/7 
Final Exam 
1:304:30 pm, Pillsbury Hall 110 
Solutions to quizzes in discussion sections: http://www.math.umn.edu/~hamdan/
Brief
answers to even numbered problems that were not to be turned in
I will post these after the corresponding homework
assignment is due.
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 fullperiod midterm exams,
to be held on Friday February 16, Monday April 2 and Friday
April 27. The final exam will be held 1:304:30 Monday, May 7. 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%, midterm exams
14% each, a smallgroup 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 unstarred, evennumbered problems will be
posted on the course website by either the TA or the professor.
Recitation Quizzes
(provisional)
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.
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 makeup
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.
******************************************************************************************************
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
Practice Midterm
Exam 1 with (very
brief) answers
Practice Midterm
Exam 2 with (very
brief) answers
Practice Midterm Exam 3 with (very brief) answers
Practice Final Exam with (very brief) answers