Math 1571H
Honors Calculus
Fall Semester 2006, 4 credits
Credit will not be granted if credit has
been received for: MATH 1142, MATH 1271, MATH 1281, MATH 1371; prereq
IT Honors office approval; meets Lib Ed req of Mathematical Thinking
Core; meets Honors req of Honors)
LECTURE:
Place: 110
Pillsbury Hall
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: 11:1512:05
M, 1:252:15 W, 9:059:55
F, or by appointment.
Discussion
Sections:
011: 10:1011:00
am TTh, 1701 Univ 16
TA: Hazem Hamdan, Office:
VinH 360,
(612) 6254392, hamdan@math.umn.edu
Office Hours: Tu, Th, 9:05am9:55am,
11:15am12:05pm, or by appointment.
012: 12:201:10 pm, TTh, AmundH 124
TA:
Hazem
Hamdan, Office:
VinH 360,
(612) 6254392, hamdan@math.umn.edu
Office Hours: Tu, Th, 9:05am9:55am, 11:15am12:05pm,
or by appointment.
Course Content
Most of this material will be taken from sections 1.5, 1.6, Chapters 2
 9, sections 17.1, 17.317.4, 18.118.4 of the text (though not
exactly in that order). I will also include some material in the
lectures that is not in the book particularly applications to
celestial mechanics (satellite and planetary
orbits, etc.) and to qualitative analysis of physical and biological
dynamical systems governed by differential equations (stable and
unstable equilibria, control).
Syllabus:
Sections  Topics 
1.5, 1.6  Functions 
2.12.5  The derivative, velocity and acceleration, limits 
18.118.4  Coordinates and vectors in 2 and 3 dimensions, dot product, cross product, lines and planes 
17.1  Parametric equations of curves 
2.6  Continuous functions and the mean value theorem 
3.13.6  Techniques for computing derivatives 
4.14.6  Applications of derivatives 
17.317.4  Velocity and acceleration in two and three dimensions 
5.25.5  Indefinite integrals and differential equations 
6.36.7  The definite integral 
7.27.8  Applications of integration 
8.18.6  Exponentials and logarithms in calculus 
9.19.5  Trigonometric functions in calculus 
Daily Schedule:
Date 
Sections 
Homework (due Thursday of following week)
Turn in starred problems. 
Tu 9/5

1.5, 1.6 
1.6
1b,2d,2e,2f,2g,2h*,2j,3c,3d,4a*, 4b*,4c*,5b,5d,5g,7c*,7d*

page 50, no. 53 

W 9/6 
2.1, 2.2 
2.2
1,2,5,6*,7,8* 
F 9/8 
2.3, 2.4 
2.3
24,25,27,30*,37,38*,39,40,41*,45 
2.4
8*,10,12*,14*,15 

M 9/11 
2.5 
2.5
4,5,6,8*,9,15,16*,18c,18d*,20a*,20b*,20c,20d,20e*,20f,20g 
W 9/13 
18.1, 18.2 
18.1
1,3,4,6,7*,8,9*,10,12*,14,15 
18.2
3,6*,7,8,9,12*,14 

F 9/15 
18.3 
18.3
1,2*,3*,4*,5,12* 
M 9/18 
18.4 
18.4
1,2*,3,4,5,6*,7,8,9,10*,11,13,14*,17, 18*,20,22,26* 
W 9/20 
2.6, 3.1 
2.6
2*,5,7,11,12*,14*,34*,35,39,40 
3.1
4,6,14*,18,22 

F 9/22 
3.1, 3.2, 
3.2
8,10,14,17,38* 
M
9/25 
3.3, 3.4 
3.3
9,14,24,26,33,36,44*,45,46 
3.4
2,3,4*,5,6,7,9,12*,21,22,24,30,34 

W 9/27 
3.5, 3.6, 
3.5
25,9,10*,29b,34*,36,37,39,40*,42,46* 
3.6
2,3,4,8,10*,12* 

F 9/29 
17.1, 4.1 
17.1
4,5,6*,8,9,10*,15 
4.1
5,12*,18,20*,2123,25,26b*,28,30a* 

M 10/2 
4.2, 4.3 
4.2
4,12*,14a*,14b*,15,16,18,19,25,27 
4.3
1,2,3,4,8*,10,11,18*,29* 

W 10/4 
Review 
pages 111114
5,9,40,41,43a,43d 
F 10/6 
Midterm 1 
Covers material in Sections
1.63.6, 18.14 and 17.1 
M 10/9 
4.4, 4.5 
4.4
2,3,4*,5* 
4.5
2,4*,5,9,10*,13 

W 10/11 
4.6 
4.6
1,2a*,5,9,10*,13 
F 10/13 
17.3, 17.4 
17.3
1,2*,3,4*,5,10*,14 
17.4
3,4*,6,8*,10,12* 

M 10/16 
5.1, 5.2 
5.2
1,6*,11,12*,13,14*,20*,21,23 
W 10/18 
5.3 
5.3
3,9,13,14*,32*,33,42*,49,56*,68*,69 
Th 10/19 
Derivatives test 

F 10/20 
5.4, 5.5 
5.4
2*,3,5,7,9,10,12*,18,19 
5.5
3,5,10*,12*,14* 

pages 188189 34,40* 

M 10/23 
6.1,
6.2, 6.3 
6.3 2,2c*,2f*,3*,5 
W 10/25 
6.4,
6.5, 6.6 
6.5 1* 
6.6
3,4,8*,10,15,16* 

F 10/27 
6.6,
6.7 
6.6 22,38,39,42* 
6.7
2,3*,4,8,9,11,13,14*,15,16,16b*,16c* 

M 10/30 
Review, 8.2 
8.2 3b, 3d, 4b,
4d, 5, 7 
W 11/1 
Midterm 2 
Covers
material through Section 6.7 
F 11/3 
8.1, 8.3 
8.3 4, 6, 12,
16*, 22*, 25a*, 25e*, 29 
M 11/6 
8.4 
8.4
1e,1h,1j,2c*,2j*,4b,4d,4g,4k,5b,5d,5f,5h,5i*,5j*,5k*,5l,16,18,21*,22b,22d*,23 
W 11/8 
7.1, 7.2, Conic Sections 
7.2
6,10,14*,15*,18,24,26,27,29 
F 11/10 
7.3 
7.3
1,1d*,2*,4*,6,7*,11,13,17,18 
M 11/13 
7.4 
7.4
1*,3,4*,5,6,7,8,9*,10 
W 11/15 
7.5 
7.5 2,4*,6,8,
Find the area of an ellipse of eccentricity e and directrix x=p, using
only the fact that you know the area of a circle to evaluate the area
integral for the ellipse*. 
F 11/17 
7.6 
7.6
2,4*,6,7,8,9,10*,11 
M 11/20 
7.7 
7.7
2,3,4*,6,8*,14,16,18*,19,21* 
W 11/22 
7.8 
7.8
4,6,8*,11,13*,14 
Th 11/23 
Thanksgiving 

F 11/24 
No class! 

M 11/27 
Review 

W 11/29 
Midterm 3 
Covers material through
Section 7.8 
F 12/1 
8.5 
8.5 6*,7,11,13*,
14 
M 12/4 
8.6 
8.6 8*, 10,
problems 44, 47 (page 290) 
W 12/6 
Kepler's laws 
Conic Sections link. 1*,
2* 
gravitational
potential 

F 12/8 
9.3, 9.4 ,9.5 
9.3 26,29,30 
9.4 24,25 

9.5
10,12,18*,20,22,24*,26*,28 

M 12/11 
Review 

W 12/13 
Review 

Th 12/14 
Final Exam 
1:30  4:30 pm, Pillsbury 110
(Covers material through Section 9.5) 
FINAL EXAM: 1:30 
4:30 pm Thursday, December 14, Pillsbury Hall 110
University mandated rule: "All students
must have their official University I.D. Card with them at the time of
the final exam and must show it to one of the proctors when
handing in their exam. The proctor will
not accept a final exam from a student without an I.D. Card."
Brief
answers to even numbered problems that were not to be turned in
I will post these after the corresponding homework
assignment is due.
http://www.math.umn.edu/~hamdan/
Solutions
to quizzes in recitation section.
Practice Midterm Exam 1 with (very
brief) answers
Practice
derivatives exam, with solutions
Practice Midterm
Exam 2 with (very
brief) answers
Practice Midterm Exam 3 with (very brief) answers
Practice Final Exam with (very brief) answers
What is special about this
course?
Throughout the one year sequence 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.
A precalculus review test (courtesy of Mike Weimerskirch). This is a good review of some of the high school math that I will expect you to know, and will not be repeating in class.
Course Assessment
There will be three fullperiod midterm exams, to be held on Friday
October 6, Wednesday November 1 and Wednesday November 29.
The final exam will be held 1:304:30 on Thursday,
December 14 as announced in the Class Schedules. 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 20%, midterm exams 15% each, final
exam 35%. There will also be
a shorter exam on 'methods of differentiation'. This exam
is given on a passfail basis and you must do at least 8 of the 10
problems correctly to pass. There is no partial credit. You may take
the exam several times, but you must pass this exam to pass
the course. The exam will be given for the first time on Thursday
October 19. Students who pass this exam on the first try will have
5 points added to their grades on the first hour exam for 8 correct
answers, 6 points added for 9 correct answers, and 7 points for 10
correct answers.
Homework
Assignments
will usually be posted on the website. The problems
which are indicated with a * are to be handed in on Thursdays of the
following week at the beginning of your
recitation period. Late homework will receive a very reduced grade (no
credit for problems already solved in class).
If it is handed in after the assignment has been graded, there will be
no credit given.
Quizzes
There will be a short quiz at the beginning of most of the
Thursday recitation periods covering homework due that day.
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, except the differentiation exam.
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.
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.
Student Academic Integrity
and Scholastic Dishonesty
Academic integrity is essential to a positive teaching and
learning environment. All students enrolled in University courses are
expected to complete coursework responsibilities with fairness and
honesty. Failure to do so by seeking unfair advantage over others or
misrepresenting someone else’s work as your own, can result in
disciplinary action. The University Student Conduct Code defines
scholastic dishonesty as follows:
Scholastic Dishonesty: Scholastic dishonesty means
plagiarizing; cheating on assignments or examinations; engaging in
unauthorized collaboration on academic work; taking, acquiring, or
using test materials without faculty permission; submitting false or
incomplete records of academic achievement; acting alone or in
cooperation with another to falsify records or to obtain dishonestly
grades, honors, awards, or professional endorsement; altering forging ,
or misusing a University academic record; or fabricating or falsifying
data, research procedures, or data analysis.
Within this course, a student responsible for scholastic
dishonesty can be assigned a penalty up to and including an "F" or "N"
for the course. If you have any questions regarding the expectations
for
a specific assignment or exam, ask.
Rules for
Limits and Derivatives
The Mean Value Theorem, Extended Mean Value Theorem and L'Hospital's Rule
Newton's Method and the Mean Value Theorem