Syllabus for Math 130, Calculus I, Section 1

           Department of Mathematics and Computer Science
           Hobart and William Smith Colleges

           Spring 2020.

           Instructor:  David J. Eck  (eck@hws.edu)
           
           Monday, Wednesday, Friday, 8:30–9:30 AM
                Room Gulick 2000.

           Lab: Tuesday, 12:15 1:45 PM
                Room Gulick 2000.

About The Course

Calculus I is a course in differential calculus, which is primarily the study of change and, in particular, of rates of change. Calculus is a fundamental tool in the sciences and social sciences, where the formulas that govern natural and social processes are often expressed in terms of rates of change. For example, Isaac Newton's famous laws of motion are expressed in terms of quantities such as velocity and acceleration. Velocity is simply the rate of change of position, while acceleration is the rate of change of velocity.

More generally, calculus is sometimes thought of as the study of the infinite and of the infinitesimal. Scientists, mathematicians, and philosophers have struggled for thousands of years to deal with the infinitely large and infinitely small. Calculus is the tool that has finally tamed these concepts, at least to some small extent. So in both theory and practice, Calculus is one of the crowning achievements in intellectual history. You should try to keep that in mind if you find yourself getting bogged down in formal rules and computational details — those things, although essential, are not at the heart of the subject.

The textbook for this course is a free textbook from openstax.org: Calculus, Volume 1 by Gilbert Strang, Edwin Hermann, et. al., which can be read on-line at

https://openstax.org/books/calculus-volume-1/pages/1-introduction

You can also download a PDF of the book, and you have the option of purchasing a hardcover print edition. (However, please note that I will not require you to bring the book with you to class and that a copy of the hardcover edition will be on reserve in the library.) For more information about the book, including a link to a student solution manual with answers to odd-numbered problems, see

https://openstax.org/details/books/calculus-volume-1

We will cover Chapters 2, 3, and 4 in the textbook. Note that Chapter 1 covers precalculus material that you should already be familiar with. I will review some of this material when we need it, and I might recommend readings from Chapter 1 from time to time for more detailed review.


Labs

Math 130 has a required "lab" component. The lab is actually a problem-solving session where you will work in a group of three or four students on a set of exercises that I provide. Groups will be set up randomly for the first lab and for a few other labs throughout the semester, to make sure that people are not always working in the same groups. Group lab reports will be due on the Friday after each lab (except for a few labs that are used to review for tests). You should not, in general, expect to complete all of the lab exercises in the lab period. If you do not, you should meet with your group outside of class to continue work.

Our teaching assistant for the labs will be senior math major Nick Mckenny.

Homework

I will assign and collect homework weekly. You are allowed and encouraged to work with other people in the class on homework, but you should always write up your own solutions in your own words to turn it. You can also get help from me and from the math intern.

To become proficient at calculus, you will need to do far more exercises than I can collect and grade. I will suggest exercises from the textbook for you to work on, in addition to the ones that I collect. The suggested problems will be odd-numbered exercises from the book. The textbook includes answers to odd-numbered exercises, and full solutions are available in the student solution manual, which you can download for free from the textbook web site. But remember that you can always come to me or to the math intern for help, even on the suggested exercises.


Tests, Quizzes, and Final Exam

There will be three in-class tests in addition to a final exam. The tests will be given on February 12, March 11, and April 15. The tests are given on Wednesdays, and the lab on the preceding Tuesday will be used at least partly for review.

There will be short quizzes at the beginning of some classes and at the beginning or end of some lab periods. Quizzes will not in general be announced in advance.

Note that while the tests and quizzes will concentrate on recent material, you are always responsible for all the material that has been covered, and questions about any of that material are always possible. For quizzes, there might even be questions on material that has been assigned for reading but not yet discussed in class.

The final exam will take place during the officially scheduled exam time for the course, which is Saturday, May 9, at 1:30 PM. The final exam will be comprehensive, with some emphasis on material covered in the last part of the course.


Grading

At the end of the semester, you will have grades for the following:

            First Test
            Second Test
            Third Test
            Homework
            Labs
            Quizzes
            Final Exam

I will include your final exam grade twice, giving a total of eight grades. The lowest of the eight grades will be dropped, and the remaining seven grades will be averaged to give your final grade for the course. Note that your final exam grade will definitely be counted for some part of your grade: If the final exam grade is your lowest grade, it will count for one-seventh of the total; if one of the other grades is your lowest, the final exam will count for two-sevenths.

I reserve the right to adjust your grade downwards if you miss more than a couple of classes without a good excuse. In my grading scale, an A corresponds to 90–100%, B to 80–89%, C to 65–79%, D to 55–64%, and F to 0–54%. Grades near the endpoints of a range get a plus or minus.


Attendance, Etc.

I assume that you understand the importance of attending class. While I do not take attendance in every class, I expect you to be present unless circumstances make that impossible. Participation in lab is particularly important, and I do take attendance at lab. If you miss a lab with a good excuse, you should discuss with me procedures for getting credit for the lab.

If you miss a quiz, test, or final exam without an extremely good excuse, you will receive a grade of zero. If you think you have a sufficient excuse for missing a test, please discuss it with me, in advance if possible; there is the possibility of a make-up test. I will not give make-up quizzes in general, but I will drop your two lowest quiz grades, so that one or two missed quizzes will not hurt you substantially.

Although it should not need to be said, I expect you to maintain a reasonable level of decorum in class. This means that there is usually no eating or drinking in class. Cell phones are turned off. There is no walking in late or unnecessary walking in and out of the room during lecture. I strongly discourage any use of technology in the classroom, including tablets and laptops.


Statements from the Center for Teaching and Learning

At Hobart and William Smith Colleges, we encourage you to learn collaboratively and to seek the resources that will enable you to succeed. The Center for Teaching and Learning (CTL) is one of those resources: CTL programs and staff help you engage with your learning, accomplish the tasks before you, enhance your thinking and skills, and empower you to do your best. Resources at CTL are many: Teaching Fellows provide content support in 12 departments, Study Mentors help you manage your time and responsibilities, Writing Fellows help you think well on paper, Q Fellows support you in courses that require math, and professional staff help you assess academic needs.

Disability Accommodations: If you are a student with a disability for which you may need accommodations, you should self-identify, provide appropriate documentation of your disability, and register for services with Disability Services at the Center for Teaching and Learning (CTL). Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website: http://www.hws.edu/academics/ctl/disability_services.aspx. Please direct questions about this process or Disability Services at HWS to Christen Davis, Coordinator of Disability Services, at ctl@hws.edu or x 3351.



Math Intern

The Colleges employ a "math intern" who is available on a regular schedule to help students in calculus and precalculus courses. This year, the intern is Sam LeGro (Hobart '19). You are encouraged to make use of his services, but remember that you should bring your questions to me first if possible. Math intern hours will be posted and will be announced in class.

Office Hours, E-mail, WWW

My office is room 313 in Lansing Hall. My office phone extension is 3398. I am on campus most days, and you are welcome to come in anytime you can find me there. Here are my tentative regular office hours but note that I am often available outside these times and that your office visits are certainly not restricted to my regular office hours!

         MWF 9:45–10:45 AM
         Tuesday 11:00‐ 12:00

My e-mail address is eck@hws.edu.

The home page for this course is http://math.hws.edu/eck/math130/index.html. This page will contain a weekly guide to the course, including assignments and labs. You will want to bookmark this page. This courses does not use Canvas.


Tentative Schedule

Here is a tentative weekly schedule of readings for this course. It covers all of Chapters 2, 3, and 4 from the textbook. The course web page will list the official readings each week. I might also suggest optional readings from Chapter 1 from time to time. We will try to keep approximately to this schedule, but it is likely that we will need to omit some of the less important topics. (For example, we will probably end up skipping Sections 4.2 and 4.9.) However, if we do that, I encourage you to read those sections anyway on your own.

Dates Topics / Readings
Jan. 22 and 24 Introduction to Calculus and to Limits
Sections 2.1 and 2.2
Jan. 27, 29 and 31 Limit Laws and Continuity
Section 2.3; Starting Section 2.4
Feb. 3, 5, and 7 Continuity continued and Formal Definition of Limit
Complete Section 2.4; Section 2.5
Feb. 10, 12, and 14 Introduction to derivatives
Section 3.1
Test on Wednesday. February 12
Feb. 17, 19, and 21 More on derivatives and basic differentiation rules
Sections 3.2 and 3.3
Feb. 24, 26, and 28 Rates of change; Trig functions and their derivatives
Sections 3.4 and 3.5
Mar. 2, 4, and 6 The chain rule; inverse functions; implicit differentiation
Sections 3.6, 3.7, and 3.8
Mar. 9, 11, and 13 Exponential and logarithmic functions and derivatives
Section 3.9
Test on Wednesday, March 11
Spring Break, March 14–22
Mar. 23, 25, and 27 Related rates; linear approximation
Sections 4.1 and 4.2
Mar. 30; Apr. 1 and 3 Extreme values; Mean Value Theorem; begin graphing
Sections 4.3 and 4.4; Starting Section 4.5
Apr. 6, 8, and 10 Graphing continued
Finish Section 4.5; Section 4.6
Apr. 13, 15, and 17 Max-min problems
Starting Section 4.7
Test on Wednesday, April 15
Apr. 20, 22, and 23 More max-min; L'Hôpital's rule; Newton's method
Finish Section 4.7; Sections 4.8 and 4.9
Apr. 27 and 29; May 1 Antiderivatives
Section 4.10
May 4 Last day of class; wrap up the course!
May 9 Final Exam: Saturday, May 9, 1:30 PM