Math 1572H  Honors Calculus
Spring Semester 2006, 4 credits

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,,,
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;
012: 10:10-11:00 am TTH, VinH 311, TA: Ryan Gantner

Course Content:

  • Methods of integration
  • Applications of integration
  • Indeterminate forms and improper integrals
  • Infinite series, power series
  • Partial derivatives, gradients, directional derivatives
  • Applications to rocket science.

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):

Methods of integration
Centroids, Center of mass             
Indeterminant forms, L'Hospital's rule, improper integrals
Infinite series
Power series, Taylor's formula
Polar coordinates revisited
Curvature and normals, Tangential and normal components of acceleration
Quadric surfaces, Cylindrical and spherical coordinates
Partial derivatives, Tangent planes, Directional derivatives and gradient
Maximum and minimum problems in several variables

Daily Schedule:

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

W    1/25

F      1/27

M     1/30

W     2/1
11.1, 11.2,

F       2/3
11.3,   Rocket Science

M      2/6
12.1, 12.2

W      2/8

F       2/10

M      2/13
Rocket Science

W      2/15

F        2/17
Midterm I

M      2/20
13.1, 13.2

W      2/22

F        2/24

M       2/27
13.5, 13.6

W       3/1

F         3/3

M       3/6
Rocket Science

W       3/8
14.1, 14.2

F         3/10

Spring Break!

M       3/20

W      3/22

F        3/24

M      3/27
16.1, 16.2

W      3/29

F        3/31
Rocket Science

M         4/3
Midterm II

W        4/5
16.1, 16.2

F          4/7

M       4/10
17.5, 17.6

W       4/12
18.6, 18.7

F         4/14

M       4/17

W       4/19

F         4/21
19.4, 19.5

M        4/24
19.5, 19.7

W        4/26

F          4/28
Midterm III

M        5/1

W        5/3

F          5/5

M        5/8
Final Exam
1:30-4:30 pm, Akerman Hall 209

FINAL EXAM:  1:30 - 4:30 pm Monday, May 8,   AKERMAN HALL 209
"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."

Quiz 1, January 26    Quiz 1 solutions

Midterm I practice exam

Midterm I (with solutions)

Midterm II practice exam

Midterm III practice exam

Practice Final Exam

What is special about this course:
This is the second semester of an honors course meant for students of science and engineering. The emphasis will be on problem solving, that is, in using calculus to solve or find approximate solutions to problems that arise in the other sciences and engineering as well as mathematics itself. This is not a theoretical course but I expect you to have an "inquiring mind" and not to accept my assertions on faith alone. Thus I will always try to make it evident why something is true. The goal of this course is to provide you with sufficient understanding and facility so that calculus becomes a basic (practical) tool that you employ in your investigation into any of the pure and applied sciences.

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 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.

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.

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

Rocket Science

1. Epicycles              Plots of epicycles

2. Conic sections in polar coordinates, Kepler's laws, and the gravitational force

3. Pythagorean triples,  trigonometric integrals, and the Kepler equation   Kepler equation plots

4. General solution of Newton's gravitational equations

5. Hyperbolic trajectories      (ps file)

6. Impulse maneuvers             Some Hohmann transfer trajectories

7. Project Loiterer II             The path of Loiterer II