Math 1571H Honors Calculus
Fall Semester 2005, 4 credits
Lecture:
Place: Rapson Hall 31
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, Pillsbury Hall
110
TA:
Hazem Hamdan, (612) 6254392, VinH 360, hamdan@math.umn.edu, 9:05am9:55am MTh, 2:30pm3:20pm F
012: 12:201:10 pm, TTh, Vincent Hall 211
TA: Hazem Hamdan, (612)
6254392, VinH 360, hamdan@math.umn.edu, 9:05am9:55am MTh, 2:30pm3:20pm F
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 
9.19.6  Trigonometric functions in calculus 
Daily Schedule:
Date 
Sections 
Homework
(due Thursday of following week) Turn in starred problems. 
Tu 9/6 
1.5, 1.6 

W 9/7 
2.1, 2.2 

F 9/9 
2.3, 2.4 

M 9/12 
2.5 

W 9/14 
18.1, 18.2 

F 9/16 
18.3 

M 9/19 
18.4 

W 9/21 
2.6, 3.1 

F 9/23 
3.1, 3.2, 

M
9/26 
3.3,
3.4 

W
9/28 
3.5,
3.6, 

F
9/30 
17.1,
review 

M 10/3 
Midterm
1 

W 10/5 
4.1,
4.2 

F 10/7 
4.3,
4.4 

M 10/10 
4.5 

W 10/12 
4.6 

F 10/14 
17.3, 17.4 

M 10/17 
5.1, 5.2 

W 10/19 
5.3 

Th 10/20 
Derivatives
test 

F 10/21 
5.4, 5.5 

M 10/24 
6.1, 6.2, 6.3 

W 10/26 
6.4, 6.5, 6.6 

F 10/28 
6.6, 6.7 

M 10/31 
8.1, 8.3 

W 11/2 
Review, 8.2 

F 11/4 
Midterm 2 

M 11/7 
8.4 

W 11/9 
7.1, 7.2 

F 11/11 
7.3 

M 11/14 
7.4 

W 11/16 
7.5 

F 11/18 
7.6 

M 11/21 
7.7 

W 11/23 
7.8 

Th 11/24 
Thanksgiving 

F 11/25 
No class! 

M 11/28 
Review 

W 11/30 
Midterm 3 

F 12/2 
8.5 

M 12/5 
8.6 

W 12/7 
Kepler's laws 

gravitational potential 

F 12/9 
9.3, 9.4 ,9.5 

M 12/12 
9.6 

W 12/14 
Review 

Th 12/15 
Final Exam 
1:30  4:30 pm, Smith Hall
331 (Covers material through Section 9.5) 
Quiz 1 with solutions (September
15)
Quiz
2 with solutions (September 22)
Quiz 3 with
solutions (September 29)
Quiz 4 with solutions (October 13)
Quiz 5 with solutions (October 27)
Quiz 6 with solutions (November 10)
Quiz 7 with solutions (November 17)
Practice derivatives exam, with solutions
Practice midterm exam 2, with (very brief) solutions
This is longer than the actual exam will be, but should be good practice.
Practice final exam, with (very brief) solutions
The number of points
for each problem will be indicated on the actual final.
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 Monday October 3, Friday
November 4 and Wednesday November 30. The final
exam will be held at the scheduled time as announced in the
Class Schedules, which is Thursday December 15, 1:304:30.
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 20. 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 in boldface
above we expect the following:
Do not use scratch paper or other low quality paper for your homework.
All four sides of the paper should have a straight edge (do not take the papers from your notebook). The best size is either A4 or A3.
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.
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.
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.
Rules for Limits and Derivatives
Newton's Method and
the Mean Value Theorem