Honors Calculus 1 - Fall 2009

COURSE: MATH 1910-088
CALL #80865
TIME AND PLACE: 9:20-10:15 MWF in Sam Wilson 322, 3:45-4:40 R in Burleson 302

INSTRUCTOR: Dr. Robert Gardner
OFFICE HOURS: 10:15-11:15 MWF
OFFICE: Room 308F of Gilbreath Hall
PHONE: 439-6979 (308F Gilbreath), Math Department Office 439-4349
E-MAIL: gardnerr@etsu.edu
WEBPAGE: http://faculty.etsu.edu/gardnerr/gardner.htm (see my webpage for a copy of this course syllabus, copies of the classnotes in PDF and PostScript formats, and updates for the course).

Primary Resources and Details

TEXTS: Thomas' Calculus, Early Transcendentals, 11th edition, by G. Thomas, R. Finney, M. Weir, and F. Giordano. The Calculus Wars by J. Bardi.

SAMPLE TESTS: Copies of old tests, along with solutions, are available through online reserve on the Sherrod Library website. Go to the ETSU Web Catalog (http://libraries.etsu.edu/), click the "Author" tab, under "In this library" use the pulldown menu to select "ETSU Sherrod Library Reserves." Enter "Gardner" in the "Look for" area and the select "Search." This will allow you access to PDF copies of sample tests. Be warned that many of the sample tests are from the standard non-honors-enhanced version of Calculus 1!

ONLINE CLASS NOTES: Class notes will be given primarily in the form of overheads. Definitions, theorems, some proofs, and a few examples will be included on the overheads. Most examples and questions concerning homework problems will be written on the board. Copies of the overheads are on reserve in the library, in the Math Lab, and online at:

http://faculty.etsu.edu/gardnerr/1910/Notes-11E/notes.htm.
It is strongly recommended that you get copies of the overheads before the material is covered in class. This will save you from writing down most notes in class and you can concentrate on listening and supplementing the notes with comments which you find relevant. The notes for the "Meaning of Mathematics" lecture are also online at:
http://www.etsu.edu/math/gardner/GIS/math-meaning.pdf.
A link to a website concerning the latest results for large twin primes is: The Top Twenty: Twin Primes.
I am in the process of posting several videos related to the Calculus 1 lectures:

ADDITIONAL RESOURCES: Instructor's Solution's Manual by M. Weir, contains worked-out solutions for all exercises in the text. Answer Book contains short answers to most exercises in the text. Student Study Guide by M. Weir, gives study tips and additional practice. Student Solutions Manual by M. Weir contains worked-out solutions to all odd-numbered exercises in the text. A copy of each of these additional resources will be on reserve in the library.

PREREQUISITES: As the ETSU catalog states, the prerequisites for this class are either two years of high school algebra and one year of plane geometry or Precalculus (MATH 1720). You must be familiar with the behavior of functions, their domains, their compositions, and piecewise defined functions. Additionally, you must either be an honors scholar or an honors-in-discipline math major.

GRAPHING CALCULATORS: "The designated calculator for Calculus I, II, and III will be the TI89. The TI92 is also suitable." [This is a departmental policy usually stated in the Schedule of Classes Bulletin.]


TI 89

TI 92
You may use the calculator on the homework assignments however you choose. However, on the tests you will be required to show all detailed work and the use of calculators on the tests is not allowed. Therefore it is probably in your best interest to minimize the use of the calculator on the homework exercises. You are here to learn calculus and the calculator will be used only as an aid. Whenever calculating derivatives, I will require that you use my "square brackets" notation. A handout will be given which illustrates this method and a version can be found online in HTML at
http://www.etsu.edu/math/gardner/1110/squareb.htm,
in PDF form at
http://www.etsu.edu/math/gardner/1920/square-brackets.pdf,
and in PostScript form at
http://www.etsu.edu/math/gardner/1920/square-brackets.ps.
You can find a handout on the application of the TI-89 in Calculus 1 online at:
http://www.etsu.edu/math/gardner/1110/ti89.pdf.

Grading and Tests

GRADING: Your grade will be determined by the average on four tests (T1-T4), the comprehensive final (F), and the Calculus Wars report and presentation (CW). Your average is determined by

AVERAGE = (T1 + T2 + T3 + T4 + CW + 2F)/7.
Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate (based on grade points assigned by the university, on a plus/minus 3 point system). There are no options for extra credit and the only way to earn bonus points will be provided on the four tests. Any questions about how a test was graded should be addressed within one week of the return of the graded test. These policies are nonnegotiable.

THE CALCULUS WARS PROJECT: We will read and discuss The Calculus Wars - Newton, Leibniz, and The Greatest Mathematical Clash of All Time by Jason Bardi. Your participation in class discussions of the book is assumed. In addition, the class will be partitioned into groups of three and choose a topic related to The Calculus Wars. The group will give a written report on the topic and an in-class presentation. The written reports are due December 7 and the presentations will be given December 7, 9, and 10. A group grade will be given with each member of the group getting the same grade. Here's some resources concerning our discussions:

  1. Calculus Wars Assignment.
  2. Timeline for Preface and Chapters 1-3.
  3. Timeline for Chapter 4.
  4. Timeline for Chapter 5.
  5. Timeline for Chapters 6 and 7.
  6. Timeline for Chapters 8 to 10.
  7. Timeline for Chapters 11, 12, and Epilogue.
Here's an online copy of "The Early Mathematical Manuscripts of Leibniz". A copy of the first use of an integral sign in Leibniz's own writing (dated October 29, 1675) is available here.
Ask the author of The Calculus Wars a question! Check out Cogito - Open for Questions: Jason Bardi, Author of The Fifth Postulate.

THE FINAL: We will have a comprehensive final on Monday, December 14 from 8:00 a.m. to 10:00 a.m.

GATEWAY EXAM: Students in Honors Calculus are not required to take the Gateway Exam.

Other Resources to Help You

MATH LAB: The Mathematics Laboratory is located in Room 309 of Warf-Pickle Hall. It is staffed by graduate students and upper level undergraduates. They are there to help you! Hours of operation are (tentatively) Monday-Thursday 11:00--7:00, Sunday 1:00-5:00. The phone number is 439-7611.

ONLINE HELP: The Addison Wesley Longman Math Tutor Center is available online at

http://www.awl.com/tutorcenter.
It provides assistance to students who take calculus and purchase a mathematics textbook published by Addison Wesley Longman. Help is provided via phone, fax, and e-mail. Students who use the service will be helped by tutors who are qualified mathematics instructors.

CD-ROM AND WEB SITE: The CD-ROM included with the text has several interactive features and tutorials. It includes video clips of real-world situations which provide motivation for learning and applying calculus. The text web site (http://www.awl.com/thomas) has the "Just-in-Time" Online Algebra and Trigonometry web-based testing and tutorial system which allows students to practice the algebra and trigonometry skills critical to mastering calculus. The Interactive Calculus Tutorial is an online tutorial which lets students review textbook-specific material by chapter through practice quizzes and diagnostic feedback on their performance. The Skill Mastery Quizzes are a collection of chapter-by-chapter quizzes on the web site which can be administered and graded online for skills-based mastery assessment.

STUDENT SUPPORT SERVICES: Student Support Services provides free individual tutoring to qualified individuals through their NEXUS program. The criteria state that the student must be: (1) a first-Generation College student, meaning, neither of your natural parents has completed a four-year college degree, (2) income eligible, or (3) a student with a documented disability. For more details, see:

http://www.etsu.edu/sss/

DESIRE2LEARN: I have created an extensive discussion list on the Desire2Learn ("elearn") website. There is a discussion forum for each section of the calculus book, each test, and each chapter of The Calculus Wars book. You can log in at: http://elearn.etsu.edu/. I will not likely post other material on Desire2Learn, but will simply post it directly on the internet.

SYLLABUS ATTACHMENT: You can find an on-line version of the university's syllabus attachment (which contains general information concerning advisement, honor codes, dropping, etc.) at:

http://www.etsu.edu/reg/documents/PDF/SYLLABUS_ATTACHMENT_fall_2009.pdf.

Additional Information

NOTE: Calculus is the "mathematics of motion." We will see many applications of the Calculus 1 material which involve motion and dynamics. Because of this connection with the physical sciences, calculus is one of the most applicable areas of mathematics. You will see many of the concepts in this class again if you take the Technical Physics sequence. This material is certainly not easy, though! You should plan on investing a great deal of time in this class. If you allot an appropriate amount of time for your studies (at least 2 hours outside of class for each hour spent in class) then I think this can be a pleasant and rewarding (intellectually and grade-wise) experience! I will post test solutions outside of my office door (in Gilbreath) after each test. As a result, I will only consider questions about how your test was graded during the week following a test.

IMPORTANT DATES:
Monday, September 7 = Labor Day Holiday.
Friday, September 11 = Last day for 75% refund.
Friday, September 11 = Last day to drop without a grade of "W."
Thursday, September 24 = Test 1 (2.1-2.7).
Thursday, October 15 = Test 2 (3.1-3.9).
Monday, October 19 = Fall Break Holiday.
Monday, October 26 = Last day to drop without dean's permission.
Thursday, November 5 = Test 3 (3.10, 4.1-4.6).
Thursday and Friday, November 26 and 26 = Thanksgiving Holiday.
Thursday, December 3 = Test 4 (4.7, 4.8, 5.1-5.6).
Monday, December 7 = Written reports due.
Wednesday, December 9 = Last day to withdraw from the university.
Friday, December 11 = Last day of class.
Monday, December 14 = Comprehensive final, 8:00 a.m. to 10:00 a.m.

Course Outline

We will follow this tentative outline. "EOO" means Every Other Odd (that is, 1, 5, 9, 13, etc.). Notice that, on average, we spend more time on the sections of the first two chapters (since this is where many fundamentally new concepts are introduced). Also notice that each test is scheduled on a Thursday.

DATE
AGENDA
HOMEWORK
MON 8/31
Introduction, The Meaning of Math
-
WED 9/2
Meaning (cont.), 2.1 = Rates of Change and Limits
2.1 = 1-33 (EOO)
THR 9/3
2.1 (cont.), 2.2 = Calculating Limits Using the Limit Laws
2.2 = 1-57 (EOO)
FRI 9/4
2.2 (cont.)
-
MON 9/7
Labor Day Holiday
-
WED 9/9
2.3 = The Precise Definition of Limit
2.3 = 1-57 (EOO)
THR 9/10
2.3 (cont.)
-
FRI 9/11
2.4 = One-Sided Limits and Limits at Infinity
2.4 = 1-77 (EOO)
MON 9/14
2.4 (cont.)
-
WED 9/16
2.5 = Infinite Limits and Vertical Asymptotes
2.5 = 1-53 (EOO)
THR 9/17
2.5 (cont.), 2.6 = Continuity
2.6 = 1-37, 45-61 (EOO)
FRI 9/18
2.6 (cont.), 2.7 = Tangents and Derivatives
2.7 = 1-33 (EOO), 37b 41b
MON 9/21
2.7 (cont.)
-
WED 9/23
Review for Test 1
-
THR 9/24
Test 1 = 2.1-2.7
-
FRI 9/25
3.1 = The Derivative as a Function
3.1 = 1-57 (EOO)
MON 9/28
3.2 = Differentiation Rules
3.2 = 1-53 (EOO)
WED 9/30
3.3 = The Derivative as a Rate of Change
3.3 = 1-29 (EOO)
THR 10/1
3.4 = Derivatives of Trig Functions
3.4 = 1-49 (EOO)
FRI 10/2
3.5 = The Chain Rule and Parametric Equations
3.5 = 1-117 (EOO)
MON 10/5
3.6 = Implicit Differentiation
3.6 = 1-69 (EOO)
WED 10/7
3.7 = Derivatives of Inverse Functions and Logarithms
3.7 = 1-97 (EOO)
THR 10/8
3.7 (cont.), 3.8 = Inverse Trigonometric Functions
3.8 = 1-89 (EOO)
FRI 10/9
3.8 (cont.)
-
MON 10/12
3.9 = Related Rates
3.9 = 1-37 (EOO)
WED 10/14
3.9 (cont.), Review for Test 2
-
THR 10/15
Test 2 = 3.1-3.9
-
FRI 10/16
3.10 = Linearization and Differentials
3.10 = 1-69 (EOO)
Calculus Wars: Preface, Chapters 1-3
MON 10/19
Fall Break
-
WED 10/21
4.1 = Extreme Values of Functions
4.1 = 1-77 (EOO)
THR 10/22
4.2 = The Mean Value Theorem
4.2 = 1-49 (EOO), 57, 65
FRI 10/23
4.2 (cont.), 4.3 = Monotone Functions, 1st Derivative Test
4.3 = 1-61 (not T) (EOO)
MON 10/26
4.3 (cont.)
-
WED 10/28
4.4 = Concavity and Curve Sketching
4.4 = 1-81 (EOO)
THR 10/29
4.4 (cont.), 4.5 = Applied Optimization Problems
Integral Day!
4.5 = 1-13, 21-57a (EOO)
FRI 10/30
4.5 (cont.)
-
MON 11/2
4.6 = Indeterminate Forms and L'Hopital's Rule
4.6 = 1-69 (EOO)
WED 11/4
Review for Test 3, Guest Lecturer
-
THR 11/5
Test 3 (3.10, 4.1-4.6) Guest
-
FRI 11/6
4.7 = Newton's Method, Guest Lecturer
4.7 = 1-11 odd, 21, 23 (EOO)
Calculus Wars: Chapters 4, 5
MON 11/9
4.7 (cont.), 4.8 = Antiderivatives
4.8 = 1-125 (EOO)
WED 11/11
4.8 (cont.)
-
THR 11/12
5.1 = Estimating with Finite Sums, Review for Test 3
5.1 = 1-21 (EOO)
FRI 11/13
5.2 = Sigma Notation and Limits of Finite Sums
5.2 = 1-37 (EOO)
Calculus Wars: Chapters 6, 7
MON 11/16
5.3 = The Definite Integral
5.3 = 1-81 (EOO)
WED 11/18
5.4 = The Fundamental Theorem of Calculus
5.4 = 1-81 (EOO)
THR 11/19
5.4 (cont.)
-
FRI 11/20
5.5 = Indefinite Integrals and the Substitution Rule
5.5 = 1-69 (EOO)
Calculus Wars: Chapters 8-10
MON 11/23
5.6 = Substitution and Area Between Curves
5.6 = 1-117 (EOO)
WED 11/25
Calculus Wars Discussion
Deadline for Choice of Calculus Wars Project
-
THR 11/26
Thanksgiving Holiday
-
FRI 11/27
Thanksgiving Holiday
-
MON 11/30
5.6 (cont.)
-
WED 12/2
Review for Test 4
-
THR 12/3
Test 4 (4.7, 4.8, 5.1-5.6)
Calculus Wars: Chapters 11, 12, Epilogue
FRI 12/4
Review for final, Calculus Wars Discussion
-
MON 12/7
Written Report Due, Group Presentations
Opticks (Colvett, Hunt, Overton)
Archimedes (Denney, Poole, Powell)
-
WED 12/9
Group Presentations
Calculus Before Newton (Catlett, Houser, Mart)
Newton's and Leibniz's Work on Calculus (Keane, Loftis, Underdown)
-
THR 12/10
Review for Final
-
FRI 12/11
Review for Final
-
MON 12/14
Final, 8:00 a.m. to 10:00 a.m.
!

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Last updated: November 23, 2009.