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)

Place:  110  Pillsbury Hall
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,   1:25-2:15  W,   9:05-9:55 F, or by appointment.

Discussion Sections:
10:10-11:00 am TTh, 1701 Univ 16

TA: Hazem Hamdan,   Office:  VinH 360,   (612) 625-4392,
Office Hours: Tu, Th,   9:05am-9:55am,  11:15am-12:05pm,  or by appointment.

012: 12:20-1:10 pm, TTh, AmundH 124
TA:  Hazem Hamdan,  Office:  VinH 360,   (612) 625-4392,
Office Hours: Tu, Th,   9:05am-9:55am,  11:15am-12:05pm,
 or by appointment.

Course Content

  • The derivative and how to calculate it.
  • Dot and cross products of vectors. Equations of lines and planes. Parametrization of curves. Functions and graphs.
  • Properties and applications of the derivative, extremal problems.
  • The integral, how to calculate it, its properties and applications, areas, surfaces and volumes.

Most of this material will be taken from sections 1.5, 1.6, Chapters 2 - 9, sections 17.1, 17.3-17.4, 18.1-18.4 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).


Sections  Topics
1.5, 1.6 Functions
2.1-2.5 The derivative, velocity and acceleration, limits
18.1-18.4 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
3.1-3.6 Techniques for computing derivatives
4.1-4.6 Applications of derivatives
17.3-17.4 Velocity and acceleration in two and three dimensions
5.2-5.5 Indefinite integrals and differential equations
6.3-6.7 The definite integral
7.2-7.8 Applications of integration
8.1-8.6 Exponentials and logarithms in calculus
9.1-9.5 Trigonometric functions in calculus

Daily Schedule:

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   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  1,2*,3*,4*,5,12*
M 9/18
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   2-5,9,10*,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*,21-23,25,26b*,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
pages 111-114    5,9,40,41,43a,43d
F 10/6
Midterm 1
Covers material in Sections 1.6-3.6, 18.1-4 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    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     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 188-189  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  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  1,1d*,2*,4*,6,7*,11,13,17,18
M 11/13
7.4  1*,3,4*,5,6,7,8,9*,10
W 11/15
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  2,4*,6,7,8,9,10*,11
M 11/20
7.7  2,3,4*,6,8*,14,16,18*,19,21*
W 11/22
7.8  4,6,8*,11,13*,14
Th 11/23

F  11/24
No class!

M 11/27

W 11/29
Midterm 3
Covers material through Section 7.8
F 12/1
8.5  6*,7,11,13*, 14
M 12/4
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

W 12/13

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.          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?

This is an honors course meant for students of science and engineering with a strong background in algebra, geometry and trigonometry. You will be expected to be able to do algebraic and trigonometric computations accurately and rapidly: the course will be devoted to calculus, not a review of what should have been learned in high school. 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 and its sequel Math 1572H 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. 

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 full-period mid-term exams, to be held on Friday October 6, Wednesday November 1 and Wednesday November 29. The final exam will be held 1:30-4:30 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%, mid-term exams 15% each, final exam 35%. There will also be a shorter exam on 'methods of differentiation'. This exam is given on a pass-fail 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.

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.

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 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, 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.

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

Rocket Science

1. Epicycles              Plots of epicycles  

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